IB Sound & Waves Booklet 2.1 - FILLED PDF

SPH3U Name: _________________________________________ APHS U4 - Sound and Waves Unit 4 - Sound and Waves *insert cartoons here*...

SPH3U Name: _________________________________________ APHS U4 - Sound and Waves Unit 4 - Sound and Waves *insert cartoons here* 0 SPH3U Name: _________________________________________ APHS U4 - Sound and Waves Waves and Vibrations/Oscillations Wave vs. Vibration wave A _____________ is defined as a disturbance that transfers energy over a distance. This definition is easily understood when considering the behaviour of common waves such as sound waves, water waves, and seismic waves. Consider the pictures, to the right, which shows how a disturbance applied to the rope travels to the right over a distance. The repeated pattern of motion that a wave (disturbance) exhibits is an periodicmotion example of the more general phenomenon ____________________________. Periodic motion can be exhibited by any object that performs the same motion over and over again. One full _____________ of this repetitive motion is called a _____________ cycle vibration or an oscillation _____________. One full vibration/ oscillation takes place when the object returns back to its original position. See the two diagrams below and determine what one full vibration is. mat Types of Vibrations There are two different types of vibrations that we will be talking about: a) Transverse vibration __________________________________ – the object oscillates perpendicular to its rest axis ○ This is like the rope diagram shown above vibration b) __________________________________ – the object oscillates parallel longitudinal to its rest axis ○ This is like the slinky diagram shown to the right 1 SPH3U Name: _________________________________________ APHS U4 - Sound and Waves Measurements of Vibrations/Oscillations The frequency _____________ of an oscillating object is the number of cycles it completes in one second. Mathematically, this is expressed as: Irpm treated Into É 8 f 0.01678C 0.016747 where N is the number of cycles and Δt is the total measured time. yes f's The unit for frequency is called the _____________ (Hz) where 1 Hz = 1 s-1. Think of a Hz as being a “something per second”. For examples, vibrations per seconds, cycles per second, revolutions per second, etc. You may have heard the common unit for frequency of RPM (revolutions per minute). Below, show how you would convert 1 RPM to a unit of Hz. (Remember: think of 1 Hz as 1 rev/sec.) period The _____________ of an oscillating object is the amount of time (usually in seconds) that it takes to complete one full cycle. Mathematically, this is expressed as: TE where N and Δt have the same meaning as they did for frequency. Looking at these two equations, it should be apparent that frequency and period are simply reciprocals of each other. This gives use the following two equations (which is really just one equation, rearranged): ft Ff Theamplitude _____________ of a vibrating object is the maximum distance away from its rest position (see the diagram on the previous page). in phase if they: Two oscillating objects are said to be _____________ period a) Have the same _____________ rest position b) Pass through the ______________________ at the same time direction c) Are traveling in the same _____________ ○ If (a) and (b) are true but this is not true and the directions are opposite then the two objects perfectly outof are ____________________________________ phase completely 2 SPH3U Name: _________________________________________ APHS U4 - Sound and Waves Example 1: A spring vibrates 15 times in 12 seconds. Find (a) the frequency and (b) the period of the spring. f Not N 15 b Font IT tf a of 125 g's 25 Es 20.8s is Hz 0.8s is1.2542 i thefrequencyofthespringvibrations thespringhasaperiodofoss thismeansthereare1,25 persecond 10.8secondspervibration Example 2: A child is on a swing and their highest point is 1.2 m from the vertical rest position. Find the total distance travelled in 3 cycles. ofacycle 211.2m 2.4m fullcycle 212.4m 4.8m i 3fall cycles 314.8m 14.4m lin g 1.2m g Fidition Homework: 1. State the type of vibration in each of the following: a. a tree sways in the wind b. a sewing-machine needle moves up and down 2. Calculate the period in seconds of each of these motions: a. a pulse beats 25 times in 15 s (0.6 s) b. a woman shovels snow at a rate of 15 shovelsful per minute (4.0 s) c. a car motor turns at 2450 rpm (revolutions per minute) (2.4 x 10-2 s) 3. A stroboscope is flashing so that the time interval between flashes is 1/80 s. Calculate the frequency of the strobe lights flashes. (80 Hz) 4. A child on a swing completes 20 cycles in 25 s. Calculate the frequency and the period of the swing. (0.8 Hz and 1.25 s) 5. Calculate the frequency and period of a tuning fork that vibrates 2.4 x 104 times in 1.0 min (4.0 x102 Hz and 2.5 x 10-3 s) 6. Calculate the frequency of the following: a. a violin string vibrates 88 times in 0.20 s (4.4 x 102 Hz) b. a physics ticket-tape timer produces 3600 dots in 1.0 min (60 Hz) c. a cd players rotates 4.5 x 103 times in 1.0 minute (75 Hz) 7. If the moon orbits the earth six times in 163.8 days, what is its period of revolution? (27.3 d) 3 SPH3U Name: _________________________________________ APHS U4 - Sound and Waves Wave Motion periodic motion by performing any sort of repeated motion. For example, a An object itself exhibits _____________ metal bar can be tied to the bottom of a string, pulled back, and then let go so it oscillates as a pendulum ____________. A different type of periodic motion that an object can be involved in is when a wave of _____________ passes energy through it. To understand this kind of periodic motion, we need to look on a smaller scale. Instead of considering the object as a whole, we need to consider the individual molecules that the object is made up of. While the wave of energy passes (or ________________) through the object, its molecules momentarily propagates move away from their resting point and then return again. In this case, the object is themedium _____________ through which the wave of energy is traveling. What was just described above is hard to visualize! Check out this wave simulation; set it to oscillate and keep an eye on the green dots. Notice how they simply move up and down. The particles that make up the medium (like a string or rope shown here) simply move up and down while the wave itself seems to move sideways. transverse wave A ___________________________ is one that moves the molecules of the medium at a right angle to the direction in which the wave/energy is traveling. DEMO: thin slinky transverse waves. crests Transverse waves create _____________ (aka positive pulses) and _____________ (aka negative pulses) troughs in the medium as they pass through it. Waves on the surface of water are an example of this. longitudinal wave A ___________________________ is one that moves the molecules of the medium parallel to the direction in which the wave/energy is traveling. DEMO: regular slinky longitudinal waves Longitudinal waves create compressions rarefactions in the medium as they pass _________________ and _________________ through it. Sound waves are an example of this (more on this later). 4 SPH3U Name: _________________________________________ APHS U4 - Sound and Waves Longitudinal waves are also hard to visualize! Check out this simulation and keep an eye on the red and green lines to see how they move back and forth in the same direction that the wave is propagating (as opposed to perpendicular directions in the case of transverse waves. Note that in the same way that transverse waves have crests and troughs, longitudinal waves instead have compressions and rarefactions. get The wavelength of a wave, identified by the Greek letter lambda λ, is the distance between any two successive identical points on the wave. xxxx Example 1: Draw 2λ of a transverse wave with A = 1.0 cm and λ = 2.0 cm. Homework: 1. A cross-section of a wave is shown in figure 7. Name the parts of the wave indicated by the letters on the diagram. 2. Measure the amplitude and wavelength of the periodic transverse wave in figure 7. 3. Measure the wavelength of the periodic longitudinal wave in figure 8 4. Draw a periodic wave consisting of two complete wavelengths, each with a wavelength of 4.0 cm a. transverse wave use a amplitude of 0.5cm b. longitudinal wave 5 SPH3U Name: _________________________________________ APHS U4 - Sound and Waves The Universal Wave Equation wave source Energy that is sent through a medium in the form of a _____________ comes from a known _____________ that constant frequency One complete oscillation of the source produces one full is oscillating at a ______________________________. ________________ in the medium. wavelength Consider the example of a human hand as the source of energy that is sent through a rope (see diagrams on page 1). A single crest or trough may be sent along the rope by making a single quick movement of the hand. If the hand continually moves up and down in an oscillatory fashion, many successive crests and troughs are formed. You can revisit this simulator from page 4 to see this. Recall the equation for constant/average speed from the kinematics unit: speed v IAE To find the _____________ (v) of a wave in a particular medium we consider that the energy travels a distance the period wavelength time equal to one ________________ (λ) in the _____________ taken to produce one full oscillation (T) – also known as _____________. Using this information and the above equation, we get the following equation: V f And since period and frequency are the reciprocals of each other, we also get: V fX universalwave equation The second version of this equation, v=fλ, is called the _______________________________________. Example 1: A water wave has a distance of 0.080 m between consecutive crests and 2.5 waves pass a given point each second. Find the speed that these water waves travel along the surface of the water.. 70.080m Vfx units vfx Hz m f 2.542 12.570.080 g m D.IM M thespeedofthesewaterwavesisO2mlg Example 2: Successive crests of a wave are 4.0 m apart. One crest goes 9.0 m in 4.5 s. Find the frequency of the waves. a 4.0m it f Y thefrequency ofthewaves FY 95 Y.fm is0 sHz od9.0m of 4.5s needtofind 0.542 6 first 2.0mg SPH3U Name: _________________________________________ APHS aperiodof U4 - Sound and Waves Example 3: It takes a particular sound wave with 1.18 x 10-3 s to travel through a point and the speed of sound through the medium is 3.4 x 102 m/s. Find the wavelength of the sound waves. 7 1.1810 s v 3.4 104 DX 1 3.410411.18403 DIE 20.4012m UT o thewavelengthoftlesoundwavesis 0.4012m Demo: Is the speed of waves constant in the same medium? Use your hand to send a single pulse through a rope or slinky with a variety of different amplitudes and frequencies. Time the pulse. Conclusion: Thespeedofanaveina particularmedium isalwaysconstant regardless ofamplitude frequency orwavelength Classwork: Understanding the Concepts 1. Calculate the speed (in metres per second) of the waves for each of the following: a. ƒ = 18 Hz, λ = 2.7 m b. ƒ = 2.1 x 104 Hz, λ = 2.0 x 105 cm c. T = 4.5 x 10-4 s, λ = 9.0 x 104 m d. T = 2.0 s, λ = 3.4 km 2. Write an equation for each of the following: a. ƒ in terms of v and λ b. T in terms of v and λ c. λ in terms of v and ƒ d. λ in terms of v and T Homework: 1. A vibrator in a ripple tank with a frequency of 20 Hz produces waves with a wavelength of 3.0 cm. What is the speed of the waves? (0.6 m/s) 2. A wave in a skipping rope travels at a speed of 2.5 m/s. If the wavelength is 1.3 m, what is the period of the wave? (0.52 s) 3. Waves travel along a wire at a speed of 10.0 m/s. Find the frequency and the period of the source if the wavelength is 0.10m. (f=100 Hz and T= 0.01 sec) 4. The period of a sound wave emitted by a vibrating guitar string is 3.0 x 10-3 s. If the speed of the sound wave is 343 m/s, what is its wavelength? (1.03 m) 5. Bats emit ultrasonic sound to help them locate obstacles. The waves a have frequency of 5.5 x 104 Hz. If they travel at 350 m/s, what is their wavelength? (6.4 x 10-3 m) 6. What is the speed of a sound wave with a wavelength of 3.4m and a frequency of 1.9 x 102 Hz? (646 m/s) 7. An FM station broadcasts radio signals with a frequency of 102 MHz. These radio waves travel at a speed of 3.0 x 108 m/s. What is their wavelength? (2.941 m) 7 SPH3U Name: _________________________________________ APHS U4 - Sound and Waves What is Sound? A sound is a form of _____________ produced by a vibrating source that is passed through the air molecules energy (longitudinally) and eventually to the auditory nerve. This may cause you to think of the classic question: If a tree falls in the forest with nobody around, does it make a sound? Humans can hear sounds produced by sources vibrating between 20 – 20 000 Hz. Sounds below 20 Hz are called infrasonic ultrasonic _____________ while those above 20 000 Hz are called _____________. Below are frequencies of common sounds and hearing ranges for animals other than humans. Activity: Try listening to this online tone generator to test the frequency range that you can hear. First, let’s test the range of the class. See the figure below for the range of hearing of various animals. Homework: 1. What frequencies would you use when designing a dog whistle and why? 2. Explain why the sound of a gun is sufficient to start and avalanche? 8 SPH3U Name: _________________________________________ APHS U4 - Sound and Waves Production and Transmission of Sound Energy medium to travel through. Like all other forms of wave energy (except for light!), sound waves need a _____________ This was first discovered in 1654 when Otto van Guericke observed that no sound was produced when a bell vacuum was rung inside a jar from which all of the air had been removed (i.e. a _____________). The diagram below shows how the vibrating tines of a tuning fork produce compressions and rarefactions in the air. Check out this simulator to see the longitudinal sound waves produced by a tuning fork. pitch The term _____________ describes how high or low a sound is perceived to be; it is really just a more subjective word for frequency. For example, a violin or a child’s scream would be considered high pitched (high frequency; more waves passing through a point per second), whereas a bass guitar or the sound of large pieces of ice breaking on a lake are a low pitch (low frequency; fewer waves passing through a point per second). Demo: Use the vernier sound sensor to visualize sound pressure of various tuning forks. a) What’s the relationship between pitch and frequency? b) What about pitch and wavelength? Homework: 1. A string on a violin is played at 8.8 x 102 Hz, and the wavelength of the sound wave is 4.1 x 10-1 m. At what speed does the sound travel in air? (3.6 x 102 m/s) 2. Calculate the frequency of a sound wave from a clarinet if the speed of sound in air is 3.4 x 102 m/s and the distance between two compressions is 1.7 m. (2.0 x 102 Hz) 3. Calculate the frequency of a sound wave if its speed and wavelength are: a. 340 m/s and 1.13 m (300 Hz) b. 340 m/s and 69.5 cm(489 Hz) 4. An organ pipe emits a note of 50.0 Hz. If the speed of sound in air is 350 m/s, what is the wavelength of the sound wave? (7 m) 5. If a 260 Hz sound from a tuning fork has a wavelength of 1.30 m, at what speed does the sound travel? (338 m/s) 6. You are on a straight road and see lightning strike the ground ahead of you. Three seconds later, you heard the thunder. If the speed of sound is 330 m/s, how far will you have to walk to reach the point where the lightning struck? (assume light travels almost instantly) (990 m) frm vfx 9 SPH3U Name: _________________________________________ APHS U4 - Sound and Waves The Speed of Sound medium whether it is gas, liquid, Sound can travel through any _____________ solids or solid. Sound typically travels fastest in _____________ , slower in liquids _____________ , and slowest in _____________. gasses This may be surprising, but it is because the molecules in a solid are more densely packed together and therefore, don’t need to travel as far to transfer the energy in the form of a longitudinal wave (and the opposite is true for gasses, and somewhere in the middle for liquids). temperature of the The speed of sound also depends on the ________________ medium. The speed of sound in common materials at 0˚C can be found in the table on the right. The speed of sound in air (v) varies with air temperature (T) and is given by the equation: Tmestbeing V 332 0,61 BECAREFUL Tis Example 1: Find the speed of sound in air at 16 C.0 temperature notperiod TEC V 332 0 IT 332 0.646 341.67s thespeedofsoundin16C air is 341.6 Homework: 1. What is the speed of sound in air when the temperature is: a. 21 degrees Celsius (344 m/s) b. 24 degrees Celsius (346 m/s) c. -35 degrees Celsius (311 m/s) 2. A 200 m dash along a straight track was timed at 21.1 s by a timer located at the finish line who used the flash from the starter's pistol to start the stopwatch. If the air temperature is 30 degrees celsius, what would the time have been if the timer had started the watch upon hearing the sound of the gun? (20.5 s) 3. How much time is required for sound to travel 1.4 km through air if the temperature is 30.0 celsius? (4 sec) 4. Compare the time it takes sound to travel 600 m in steel with the time to travel the same distance in air at 0 degrees celsius. (0.12 s and 1.8 s) 5. A fan at a baseball game is 100 m from the home plate. If the speed of sound is 350 m/s, how long after the batter actually hits the ball does the fan hear the crack? (0.29 s) 10 SPH3U Name: _________________________________________ APHS U4 - Sound and Waves The Intensity of Sound loudness The _____________ soundintensity of a sound can be quantified by measuring something called the ________________________. area 2 Although it is more formally defined as the amount of _____________ produced per unit _____________ (W/m ), power sound intensity is essentially a measure of how much sound energy hits a given point in space. The intensity of a sound received by a human ear depends on two factors: a) the _____________ of the source power from the source b) the _____________ distance This can be hard to imagine, but sound waves do not travel in these straight lines that have been depicted in earlier diagrams of longitudinal waves. Instead they travel outward from a source in spherical wave fronts (whoa…). This is why you can hear a sound from any direction around the source that it came from. Since sound waves travel out in these spherical wave fronts from the source, the surface area over which the wave’s energy is spread gets larger and larger very fast as they move outwards. Therefore, as a person moves smaller farther away from the source of a sound, the intensity of the sound arriving at their ears gets _____________ very fast. See the diagram below for a depiction of how this works. Note in the diagram above, as the sound wave moves out from a source, its energy is spread more and more thinly. (Demo: blowing up a balloon with a sharpie square on it.) The formula used to determine the intensity I distance (r) from the _____________ (I) of sound at a particular radial _____________ source is defined as the rate of _____________ as it passes through a surface with an _____________ (A) power area perpendicular to the wave’s direction, and is known as the inverse square law: I I Asphere 4T And since the area covered is that of a sphere, we get the following equation: I Ip What must the units be for intensity? units 11 SPH3U Name: _________________________________________ APHS U4 - Sound and Waves If you wanted to compare the sound intensity of the same source from two different distances, you would end up with the following equation (let’s also derive it really quick): Ratios of intensities can be used to compare intensities from a single source. É Example 1: A helicopter hovers overhead during an airshow, causing sound waves to emanate uniformly. If the first listener is 700 m away and the second listener is 1000 m away, by how much has the intensity level of the sound decreased when it reaches listener 2? See the diagram to the right r 700m IIE 109 2 2.04 FIOOOM listener I hearsasoundintensityabouttwiceasgreataslistener 2 i I 2.0412 2 decreased 12 0.491 thesoundintensityhascompared byabouthalfwhenitreacheslister listener 1 o to decibel (dB), and 0 dB is the threshold for ___________. The more common unit of sound intensity is the _____________ hearing The decibel scale is a logarithmic scale (like the Richter scale for measuring the intensity of earthquakes), meaning that a change of ten units corresponds to a ten-fold increase in the intensity. Let’s try to wrap our minds around that: 10 dB is times the intensity of 0 dB 20 dB is 190 times the intensity of 10 dB and 100 times the intensity of 0 dB 30 dB is 10 times the intensity of 20 dB and 1000 times the intensity of 0 dB 70 dB is 10000 times the intensity of 30 dB and 10000000times the intensity of 0 dB 107 130 dB is 1013 times the intensity of 0 dB (painful to the human ear) 10000000000000 Demo: Bring your headphones/earbuds/AirPods/etc. in and use the decibel meter to see the volume setting you use, then try and set the volume at the safe range, which is about 85db. Now you know what setting will be safer. Homework: 1. Why are pitch and frequency similar to loudness and intensity? 2. Normal breathing has an intensity of 10 dB. What would the intensity be if it were 10 times louder? 100 times louder? (20 dB and 30 dB) 3. A bell is run at a sound intensity of 70 dB. A trumpet is blown at an intensity level of 110. How many times more intense is the trumpet compared to the bell? (10000 times) 12 SPH3U Name: _________________________________________ APHS U4 - Sound and Waves The Reflection of Sound Waves Sound waves, like all other waves, obey the law of reflection (i.e. when a sound wave hits a rigid obstacle, the angle of incidence equals the angle of reflection). directions from the Recall that sound waves travel in all ________________ echo source. After hearing a sound, an _____________ may be heard a short time later due to sound waves that initially traveled in a different direction being reflected off a rigid surface toward you. Echoes can only be heard distinctly if the time delay is at least 0.1s. It turns out that this requires the reflecting surface to be at least 17 m away from you. Applications of echoes include: a) animals like orca whales, dolphins, bats and owls using echolocation ________________ to navigate, communicate and hunt sonar b) using _____________ to measure distances to the bottom of the ocean, submarines, schools of fish, etc x rays c) using high energy _____________ to image bone mass (with negative side effects) ultrasound to d) using slightly lower energy ________________ image soft tissue or even to promote healing and relieve pain in soft tissue as the portion of the energy that is absorbed creates a deep-heat treatment called diathermy A Example 1: Ship in 120 m water sends sonar to bottom. It returns in 0.16 s. What is the speed? data 2420m edge 240m hÉÉaed Rom ot O.lk 24th 1500ms i thespeedofthesonaris 1500mg **homework for this section is on next page** 13 SPH3U Name: _________________________________________ APHS U4 - Sound and Waves Homework: 1. A student stands 86 m from the foot of a cliff, claps her hands, and hears the echo 0.5 seconds later. Calculate the speed of sound in air. (344 m/s) 2. A pulse is sent from a ship to the floor of the ocean 420 m below the ship; 0.6 s later the reflected pulse is received at the ship. What is the speed of sound in the water? (1,400 m/s) 3. A sonar device is used in a lake, and the interval between the production of a sound and the reception of the echo is found to be 0.4 s. The speed of sound in water is 1500 m/s. What is the depth of the water? (300 m) 4. Ultrasonic sound is used to locate a school a fish. The speed of sound in the ocean is 1.48 km/s, and the reflection of the sound reaches the ship 0.12 s after it is sent. How far is the school fish from the ship? (89 m) 5. A woman makes a sound and, 3.5 s later, the echo returns from a nearby wall. How far is the woman from the wall, assuming that the speed of sound is 350 m/s. (612.5 m) 6. A man drops a stone into a mineshaft 180 m deep. If the temperature is 20.0 degrees celsius, how much time will elapse between the moment when the stone is dropped and the moment when the sound of the stone hitting the bottom of the mineshaft is heard? (6.6 s) 7. A ship traveling in a fog parallel to a dangerous, cliff-lined shore. The boat whistle is sounded and its echo is heard clearly 11 s later. If the air temperature is 10 degrees celsius, how far is the ship from the cliff? (1860 m) 14 SPH3U Name: _________________________________________ APHS U4 - Sound and Waves The Doppler Shift and Supersonic Travel Sound, just like speed, is relative to the observer (meaning measurements of it will turn out different depending on whether or not the observer is moving). Doppler The fact that the frequency of a sound changes in relation to an object’s motion is called the _______________ Effect ______________. The following diagrams depict this phenomenon in which the moving source seems to ‘catch up’ to the wavefronts in front of it and ‘run away’ from the wavefronts behind it: Demo: Set up various scenarios with this simulator Situation 1: Stationary sound source Observer A Source Observer B (Hears 500 Hz) (Producing 500 Hz) (Hears 500 Hz) Situation 2: Moving sound source Observer A Source moving to the left Observer B (Hears > 500 Hz) (Producing 500 Hz) (Hears < 500 Hz) You hear a higherfreq You hearalowerfreq asthesourceemitting as thesourceemitting thesound movestoward thesound moves away Fromyou you highpitch Vfx This explains why you hear a very ___________________ sound for an ambulance’s siren as it approaches you, lower and then a much ___________________ pitch sound after it has passed you. The only moment you hear the true pitch of the siren is when it is directly in front of you. Follow the process at each position explained below: Observer A At the source Observer B Source is approaching You Directly in front of the source Source is going away from you Wavelengths get shorter Wavelengths stay the same Wavelengths get longer Frequency increases Frequency stays the same Frequency decreases Hear a higher pitch Hear the true (actual) pitch Hear a lower pitch 15 SPH3U Name: _________________________________________ APHS U4 - Sound and Waves The concept of the Doppler Effect is very redshift similar to the concept of _____________ blueshift and _____________ of stars. As a star moves closer to us in the universe, we observe it as slightly “bluer” (blueshift) than its true colour because it is moving in the same direction as its light waves that are coming toward us. Conversely, a star that is moving away from us is observed as slightly “redder” (redshift) for just the opposite reason. Calculating the Effects of the Doppler Effect If we know the speed of sound in a medium (v), we can calculate the frequency of that sound according to an observer (fO) moving with its own speed (vO) that will be heard when the source that is producing a frequency (fS) is moving at a speed (vs): stickynote - apparent frequency according to the observer - actual frequency of the source - speed of sound waves in the given medium - speed of the source - speed of the observer ○ +ve when source is moving AWAY from observer ○ +ve when observer is moving TOWARD source ○ -ve when source is moving TOWARD observer ○ -ve when observer is moving AWAY from source ** NOTE: This equation is different from the one on your formula sheet; we will use this one. This would be a good equation to add to your sticky note (as well as how to use it). Example 1: A car driving at 100.0 km/h honks a 440 Hz horn as it approaches a stationary hiker on the side of a road. The air is 0 °C. a) What frequency does the hiker hear as the car is approaching? b) after the car is driving away? Vs1004mg27.7 fo b fo fs u Fsfg a Fs 44047 4401332,1 4401333227.7 Vo OMG 48042 40GHz 7 02 1 332 0.67 frequencyof480 asthecaris 332 0.610 i thethehikerhearsa apprachigand 10GHz as itdrives away 3324s The Doppler Effect can be used to measure the speed of objects (such as cars or baseballs) that move toward/away from a stationary source of waves. Waves of known frequency are bounced off of the moving object and the reflected waves are collected and analyzed to see how much their frequency has been shifted. 16 SPH3U Name: _________________________________________ APHS U4 - Sound and Waves Mach Number than Mach 1 have subsonic Mahl An object travelling at the speed of sound is said to be travelling at _____________. Objects travelling slower _____________ speeds; those travelling faster have _____________ speeds. The Mach number supersonic of an object is given by: Example 2: At an altitude of 10 km the speed of sound is 1060 km/h. What is the Mach number of a plane that is flying this altitude at a speed of 1800 km/h? 1060kmh Mach sound flint i theplane isflying at Mach1.7 Vaject 1800kmh 1895dg it When an object travels at the speed of sound the sound wavefronts pile up in front of the plane, producing sound barrier a ________________________ (see Figure 4b below) that is difficult to break through. If an object is able to break through this sound barrier, it will leave a noise cone __________________ boom (see Figure 4c) behind it and a __________________ sonic will be heard by outside observers. Check it out this video for more on this! To see some moving graphics of this idea as well as a simulator, check out this link! Homework: 1. You are standing at a railway crossing. A train approaching at 125 km/hr sounds its whistle. If the frequency of the whistle is 442 Hz and the air temperature is 20 degrees celsius, what frequency do you hear when the train approaches you? When the train passes you? (492 Hz, 401 Hz) 2. A car sounds its horn (502 Hz) as it approaches a pedestrian by the side of the road. The pedestrian has perfect pitch and determines that the sound from the horn has a frequency of 520 Hz. If the speed of sound was 340 m/s, how fast was the car travelling? (11.77 m/s) 3. What is the Mach number of an aircraft travelling at sea level at 0 degrees celsius with a speed of 1440 km/hr and 920 km/hr? (1.2 and 0.77) 4. A military interceptor airplane can fly at Mach 2.0. What is its speed in km/hr at sea level on a 0 degree celsius day? (2390 km/hr) 5. What is the Mach number of a plane travelling at each of the following speeds at sea level in a air with air temperature of 12 degrees celsius: 1020 m/s, 170 m/s and 1836 km/hr (3, 0.5, 1.5) 17 SPH3U Name: _________________________________________ APHS U4 - Sound and Waves Interference of Waves When two waves are headed towards each other in a medium, they experience wave interference ____________________________. If a crest and a trough encounter each other, destructive they experience ____________________ interference. If the waves have an identical amplitude and wavelength, they will cancel _____________ each other out completely, creating a point called a node _____________. The waves will then continue to pass through each other. See Figure 1 to the right. Conversely, if two crests or two troughs are headed towards each other, they constructive experience ____________________ interference. Two crests will add together to form a ____________________ supercrest and if two troughs add together they super will form a ____________________. trough The waves will then continue to pass through each other. See Figure 2 to the right. Demo/Activity: Use a slinky to demonstrate destructive interference (where a crest and a trough cancel each other out and make a node) as well as both types of constructive interference (i.e. creating a supercrest and a supertrough). See Figure 3 below to see how different shaped waves will add constructively or destructively. 18 SPH3U Name: _________________________________________ APHS U4 - Sound and Waves Classwork: 1. State whether the interference is constructive or destructive when a. a large crest meets a small trough b. a supertrough is formed c. a small compression meets a large compression 2. Use the principle of superposition to determine the resulting pulse when the pulses shown are superimposed on each other. (The point of overlap should be at the horizontal midpoints of the pulses.) Homework: 1. Figure 6 shows two pulses approaching one another. Sketch the appearance of the medium when the two pulses overlap, centres coinciding. 2. Two pulses move toward each other as shown in Figure 7. Sketch the resultant shape of the medium when the two pulses overlap, centres coinciding. 3. For Figure 8, determine the resultant displacement of the particles of the medium at each instant, using the principle of superposition. 4. What happens when two billiard balls, rolling toward one another, collide head on? How does this differ from two waves or pulses that collide head on. 19 SPH3U Name: _________________________________________ APHS 440Hz A U4 - Sound and Waves Mechanical Resonance Every object has a natural frequency at which it vibrates. When an object experiences a periodic force of the same frequency as its natural frequency, there is constructive interference on every oscillation, and the amplitude of the vibration continually increases. This phenomenon is called resonance _______________. If the underlined sentence above seems confusing, consider when a person is pushed on the swings. You don’t give them a push when they are mid-swing! You give them another push (periodic force) every time they return back to you (same frequency), which causes them to go higher and higher (constructive interference on every oscillation; increasing amplitude on each vibration). Check out this video on the Tacoma Narrows Bridge collapse in 1940, where the gusts of wind matched the natural resonant frequency of the bridge itself! Check this video on how to break a glass with sound (maybe even your voice) by matching its vibrating frequency. 85 4 Homework: 1. Consider the following: a. Every playground swing has its own resonant or natural frequency. What does frequency depend on? b. To obtain a large amplitude of vibration, how does the frequency of the input force compare with the resonant frequency? Explain. 2. When crossing a footbridge, some students notice that the bridge moves up and down. One student suggests that they all jump up and down on the bridge at the same time. Explain why this is a dangerous idea. 3. Try this: a. How would you design an experiment to determine how the resonant frequency of a long stemmed glass depends on the amount of water in the glass. b. Predict the relationship in (a). c. With your teacher’s approval, try your experimental design and describe what you discover. 4. Provide some examples of mechanical resonance. 5. Your car is stuck in ruts in the snow. How could you use the principle of resonance to free it? 20 SPH3U Name: _________________________________________ APHS U4 - Sound and Waves Standing Waves amplitudeand wavelength A special case of wave interference in a 1-D medium is when waves of equal _____________ _____________ are travelling through the medium in opposite _____________ directions. The waves moving in one direction are always created by a constant _____________ source at one end, and the waves moving in the other direction can be from the reflected off of a free end, reflected off a fixed end, or created by a second (and original source’s waves _____________ equal) constant source at the other end. areasof CONSTRUCTIVE areasofPESTMYYIM interference standing wave way The result of this interference is something called a ____________________________. A standing wave consists of antinode points called _____________ that do not move at all and areas in between nodes called _____________ that oscillate between supercrests ________________ and super ________________. How these parts of a standing wave are created is troughs depicted in the diagram below. in IX 21 Thedistance bw 2 successivenodes isEX SPH3U Name: _________________________________________ APHS U4 - Sound and Waves modes of vibration An example of various different __________________________________ at one end with the other end fixed is depicted below. for a string with a single vibrating source 2nodes antinode 3 nodes Zantinodes 4nodes 3antinodes Snodes Yantinodes For a given medium only certain frequencies will result in a standing wave. halfthe EX Note as well, that in all diagrams above the internodal distance is always equal to __________________________. wavelength Example 1: Two successive nodes 10 cm apart in a standing wave from a 30 Hz source. Find λ and speed. A 10am Exo 120am VFX 3071015 0.2m It 6M f 3OHz o go 22 SPH3U APHS EE.EEEEEEE Name: _________________________________________ U4 - Sound and Waves ACTIVITY: Create standing waves in the hall using a slinky with a length of 10 metres between ends. Make standing waves with 2 nodes (one at each end), 3 nodes (one more node in the middle) , 4 nodes, and 5 nodes. Measure and record the period and fill in the table below. Use these measurements to answer the question: Does the speed in a string of fixed length and tension have the same speed? Nodes Length L Wavelength Period T Frequency Speed (Harmonic) (m) (m) (s) 10cycleskycle (Hz) f (m/s) U FX 2 nodes (First) x 10 20 14.12 1.412 0.708 14.1 3 node (Second) 10 10 7.13 0.713 1.403 14.03 4 nodes (Third) 1 10 6.67 4.81 0.481 2.079 13.86 5 nodes (Fourth) 2X 10 X 5 3.600.360 2.778 13.89 Homework: 1. A standing wave interference pattern is produced in a rope by a vibrator with a frequency of 28 Hz. If the wavelength of the waves is 9.5 cm, what is the distance between successive nodes? 2. The distance between the second and fifth nodes in a standing wave is 59 cm. What is the wavelength of the wave? What is the speed of the wave of the source that has a frequency of 25 Hz? 3. The distance between adjacent nodes in the standing wave pattern in a piece of string is 25.0 cm. a. What is the wavelength of the wave in the string? b. If the frequency of the vibration is 2.0 x 102 Hz, calculate the speed of the wave. 4. You have one long piece of rope and a stopwatch. Devise a procedure to calculate the period and frequency of a standing wave with one, two, and three antinodes. Answers: 1.) 4.75 cm 2.) 39 cm; 9.8 x 102 cm/s 3.) (a) 50.0 cm (b) 1.0 x 104 cm/s More practice! 1. Draw a scale diagram of a standing wave pattern on an 8.0 m rope with four antinodes between the ends. What is the wavelength of the waves that produced the pattern? 2. 2.51 8 Lam I FEe The speed of a wave in a 4.0 m rope is 3.2 m/s. What is the frequency of the vibration required to produce a standing wave pattern with: if.IE mf f fiI a. 1 antinode? b. 2 antinodes? c. 4 antinodes? 3. ftp x 4moX 2mF 3E 6E l Standing waves are produced in a string by two waves travelling in opposite directions at 6.0 m/s. The distance between the second node and the sixth node is 82 cm. Determine the wavelength and the frequency of the original waves. F imiti.IE nii EIIm 1 0.82m I F 1463H 23 SPH3U Name: _________________________________________ APHS U4 - Sound and Waves Music & Musical Scales puretone In music, a ________________ is a sound where only one frequency (or tone) is heard. However, musical chord sounds typically consist of >1 different tones played at once; this is called a _____________. However, there is a unison special case where >1 identical tones are played at once; this is called _____________. Two or more different tones produce a harmonious (nice or pleasing) sound if their frequencies are in a simple ratio (i.e. can be reduced to a fraction with low numbers). Such two-note chords are said to have high _______________; two-note chords unlike this, that sound displeasing, are said to have high dissonance consonance ________________. Easoundsnice Isoundenotsonice octave is a tone that is double (or half) the frequency of another tone. Musically, these are the An _____________ same note. For example, there are eight (8) C notes on a piano. Let’s mark them down on the piano below and state each of their frequencies. (Hint: Middle C is about 256 Hz) 3242 6442 1287k 25642 51242 102442 204842 409GHz The scientific musical scale uses 256 Hz as the “standard frequency” , but 440 Hz is used in the musician’s musical scale as the note to tune instruments to (however, this changes depending on where you are in the world). Homework: 1. For a sound wave with a frequency of 220 Hz, determine the frequency of a sound that is a. One octave higher b. One Octave lower 2. For each pair of notes listed, determine the ratio of their frequencies as a simple fraction, then determine which pair has the higher consonance. a. 600 Hz and 400 Hz b. 800 Hz and 700 Hz Answers: 3(a) 440Hz; 3(b) 110 Hz; 4(a) 3:2; 4(b) 8:7 24 SPH3U Name: _________________________________________ APHS U4 - Sound and Waves Modes of Vibration & Quality of Sound Modes of Vibration, Harmonics, and Overtones Recall that a vibrating string (like the 10 m long slinky) can produce a variety of different standing wave patterns. For a string that is fixed at both ends, like that of a guitar or piano, there are special names we use to describe these different modes of vibration __________________________. The fundamental mode __________________________ flantinade Gods contains one loop between the fixed ends, and the sound this mode fundamental produces is called the __________________________ frequency(f0). All other modes of vibration (i.e. those with 2 or more loops) are called overtones _____________. These are whole number multiples of the fundamental frequency: 2 f0, 3 f0, etc. Since the frequencies that produce standing wave patterns are the ones that make nice musical sounds first harmonics The fundamental frequency is also known as the _____________ harmonic. they are also called _____________. third fourth harmonic of a string. This is also called the _____________ Below is a diagram that depicts the _____________ overtone. Quality of Sound The _____________ of a musical note depends on the number and relative intensity of the overtones being quality produced along with the f0. This property is what allows us to differentiate the same note being played on different instruments. The diagram below shows the waveform for a number of different instruments. Note that each instrument has a distinctly different periodic (repeating) wave. This wave repeats at a frequency equal to the corresponding note being played (e.g., an A note at 440 Hz – 440 waves per second). Also keep in mind that sound waves are still these complex spherical _________________ longitudinal waves with areas of compression ________________ and rarefaction ________________, but they can be depicted as transverse waves on a screen/page to make them easier to comprehend. 25 SPH3U Name: _________________________________________ APHS U4 - Sound and Waves Demo: Use the sound sensor to test the quality of sound of different instruments. Try to note the things discussed above. Take a look at the x-axis; see what you can determine about each wave. Example 1: A cello string 1.4 m long resonates with waves that travel at 820 m/s. Complete the following chart for the first six resonant frequencies (modes of vibration). Names Diagram Wavelength Frequency (use the full space as if the string is the width of the cell) Hz is 1st Harmonic 8 293 Fo 2nd Overtone 3fo Ufo i annexation j Iii 4th Overtone Sfo 0,56 1464 5th Overtone M's of Ex.2: Find the frequency of the 3rd overtone of a 0.75 m violin string whose waves travel at 764 m/s. 3rdovertone 72completewaves v 764ms 0.75m V fl 2 2037.3342 f D 0.375m Y 894744 g **Classwork & Homework on next page** 26  SPH3U Name: _________________________________________ APHS U4 - Sound and Waves Classwork: 1. What does the quality of a musical note depend on? 2. For each pair of sounds named below, choose the one that has the higher quality of sound. a. a high consonance sound; a high dissonance sound b. a pair of sounds with the ratio of frequencies of 9:8; a pair of sounds with a ratio of frequencies of 3:2 c. a pair of sounds consisting of f0 and 5f0; a pair of sounds consisting f0 and 2f0 3. A certain string of length 36 cm has a fundamental frequency of 310 Hz. a. Draw sketches of this string when it is vibrating in the fundamental mode, the first overtone, and the second overtone. Label the sketches. b. Determine the frequency of the string in the first and second overtone modes. c. Where are the nodes located on the string when the string is vibrating in the second overtone mode? Answers: 3.) (b) 6.2 x 102 Hz; 9.3 x 102 Hz (c) 12 cm; 24 cm Homework: 1. The fundamental frequency of a string is 220 Hz. Determine the frequency of the a. second harmonic b. fourth harmonic 848 BTW thesewouldboth octaves c be b thefo isdoubled andthendoubled again 2. The note A (f = 440 Hz) is struck on a piano. Determine the frequency of the following: a. The second harmonic 880 Hz b. The third harmonic c. The fifth harmonic 28th 3. Use the principle of superposition to add the following waves. Describe how the resulting waveform relates to the quality of the musical sound. a. Wave X: λ = 6.0 cm, A = 2.0 cm (Draw one wavelength.) b. Wave Y: λ = 2.0 cm, A = 1.0 cm (Draw three wavelengths to coincide with Wave X.) 4. Assume that a 900-Hz note is the third harmonic of a sound. What are the first, second, and fourth harmonics? 3rd harmonic 3f 313930Hz harmonic fundamentalfreq 1st fo 300Hz Lfo 60047 2ndharmonic 1kW 4fo 120042 4ᵗʰLarmonic REEF 27 addtheamplitudesofftheredbluewaves Wully Resultingwave Xty just tofindthesepointsconnect thedots ateachgridlineand SPH3U Name: _________________________________________ APHS U4 - Sound and Waves Resonance in Air Columns DEMO: Use a 512 Hz and 1024 Hz tuning fork with an adjustable closed air column to demonstrate the specific resonant lengths. SIMULATION: As we work through this lesson, we will be drawing sound waves as transverse waves. These waves are obviously longitudinal, but that is very difficult to draw. This simulator does a good job of showing the longitudinal and transverse waves side by side to see what is actually being depicted with a transverse wave. Check it out for review after the lesson! column air When sound waves are sent down an __________________, the waves that reflect off one end interfere with the waves that are still on their way down (just like fixed end reflections in a rope). With a rope, we got a standingwave when the perfect combination of _____________ __________________ frequency and the length of the medium gave us perfect ½ integer multiples of wavelengths. Similarly, in air columns, the perfect combination of frequency and column length will give us wavelengths of increasing ½ integer multiples to create standing waves within the column. However, another factor that comes into play is whether the ends of the column are closed _____________ or _____________. open NOTE: To achieve resonance in any type of air column, a standing wave must form such that a ________ node is formed at any closed end and an antinode _____________ is formed at any open end. Closed Air Columns (closed at one end only) When a certain frequency is played into a closed air column and the sound waves reflect off the closed end such that a standing wave is formed with a _____________ at the nodeantinade closed end and an _____________ at 1st resonant y ii Etihad the open end we get _____________. resonance This means at any of these lengths, the given frequency will be heard Hmmmmm title 1.1 loudly (resonate). On the right, C draw the first three standing waves that fulfil this criteria to show that length this happens when the length of the air column is ¼λ, ¾λ, 1¼λ, 1¾λ, etc. Ienantlength Example 1: A tuning fork is held near a water-filled column. The water is slowly lowered and the first loud sound is heard at 9.0 cm. Determine the (a) λ of the tuning fork and the (b) 2nd resonant length. resonantlength 34130 4 419 4344 27cm 4D 36cm tx I.am EX 28 SPH3U Name: _________________________________________ APHS U4 - Sound and Waves Example 2: The 1st resonant length of a closed air column is 16 cm. a) What is the λ of the sound? b) If the frequency of the sound is 512 Hz, what is the speed of the sound wave in the column? c Whatisthetemperatureoftheroom c v332 0.67 f Vfx a 4 16 b SIZHz 512710.64 T FEWIban 1 446 64cm 327.68ms V3 64cm g gym Open Air Columns (open at both ends) When sound waves of a particular frequency are sent down an open o p air column, they reflect off the k open end such that a standing wave is formed with an antinode ____________ at both open ends. When antinodes are created at both open ends we get resonance. On the right, draw the first three standing treat off waves that fulfil this criteria to show that this happens when the length of the air column is ½λ, 1λ, 1½λ, 2λ, i etc. 2ndresonant Example 3: A 3.6 m organ pipe length makes note at f0. a) What is the wavelength of note? b) If the speed of sound in the pipe is 346m/s, what is the fundamental 3rdresonant frequency? length c) What is the wavelength of the third overtone? All string instruments (guitar, cello, violin, bass) vibrate as strings (what a surprise!), all brass instruments (trumpet, trombone, tuba) vibrate as open air columns, and some woodwind/reed instruments (oboe, saxophone, clarinet) vibrate as closed air columns. The human voice is also a case of a closed air column. **Classwork & Homework on next page** 29 SPH3U Name: _________________________________________ APHS U4 - Sound and Waves Homework - Closed Air Columns: 1. The first resonant length of a closed air column occurs when the length is 30.0 cm. What will the second and third resonant lengths be? 2. The third resonant length of a closed air column is 75 cm. Determine the first and second resonant lengths. 3. What is the shortest air column, closed at one end, that will resonate at a frequency of 440 Hz when the speed of sound is 352 m/s? 4. A signalling whistle measures 5.0 cm from its opening to its closed end. Find the wavelength of the sound emitted and the frequency of the whistle if the speed of sound is 344 m/s. 5. The note B4 (f = 494 Hz) is played at the open end of an air column that is closed at the other end. The air temperature is 22 degrees C. Calculate the length of the air column for the first three resonant sounds. 6. A tuning fork causes resonance in a closed pipe. the difference between the length of the closed tube for the first resonance and the length for the second resonance is 54.0 cm. If the frequency of the fork is 320 Hz, find the wavelength and speed of the sound waves. 7. An organ pipe resonates best when its length if λ/4. Three pipes have lengths of 23.0 cm, 30.0 cm. and 38.0 cm. a. Find the wavelength of the sound emitted by each pipe. b. Find the frequency of each pipe, if the speed of sound is 341 m/s Answers: 1.) 30 cm; 90 cm; 150 cm 2.) 15 cm; 45 cm 3.) 20.0 cm 4.) 1.7 x 103 Hz 5.) 17.5 cm; 52.4 cm; 87.5 cm 6.) 1.08m; 346 m/s 7.) (a) 92.0 cm; 1.2 x 102 cm; 152 cm (b) 371 Hz; 284 Hz; 224 Hz Homework - Open Air Columns: 1. What is the length of an open air column that resonates at its first resonant length with a frequency of 560 Hz? (The speed of sound is 350 m/s) 2. The second resonant length of an open air column is 48 cm. Determine the first and third resonant lengths. 3. An organ pipe, open at both ends, resonates at its first resonant length with a frequency of 128 Hz. What is the length of the pipe if the speed of sound is 346 m/s? 4. A 1.0 x 103 Hz tuning fork is sounded and held near the mouth of an adjustable column of air open at both ends. If the air temperature is 20.0℃, calculate the following: a. the speed of the sound in air b. the wavelength of the sound c. the minimum length of the air column that produces resonance 5. A closed air column is 60.0 cm long. Calculate the frequency of forks that will cause resonance at: a. the first resonant length b. the third resonant length (The speed of sound is 344 m/s) 6. In an air column, the distance from one resonance length to the next is 21.6 cm. What is the wavelength of the sound producing resonance if the column is: a. closed at both ends? b. open at both ends? 7. What vibrates to create sound in a column of air? 8. How would a higher air temperature affect the lengths of the resonating air column? Why? 9. When water is added to a bottle, what happens to the pitch of the sound as the water is added? Explain why. Answers: 1.) 0.3125 m, 2.) 0.24 m, 0.72 m, 3.) 1.35 m, 4.) A: 343.8 m/s, B. 0.34 m, C. 0.17 m, 5.) wavelength is 2.4 m and f is 143.3 Hz, 3rd wavelength is 0.48 m and the frequency is 716.67 Hz, 6.) A. 43.2 cm and B 43.2 cm, 7. air particles, 8.) increase the lengths, 9.) Pitch increases 30 SPH3U Name: _________________________________________ APHS U4 - Sound and Waves Interference of Waves in 2-D The interference pattern between waves from two (2) point sources vibrating in phase (or coming from the same source and sent through two slits) is shown below. You can picture this as two droplets of water falling into a calm pond at a constant distance from each other and at an identical frequency (in phase). You could also picture this as waves in the ocean crashing up against a barrier with two slits in the barrier, allowing the wave to pass through in just those two spots. This is the pattern that would appear. Study it carefully and look for patterns. Let’s point out some important features. Areas of destructive interference (where a crest [solid line] meets a trough [dotted line]) create nodes ___________. nodal lives The pattern shows that nodes tend to ‘line up’ and create __________________ that radiate away from the sources. All nodal lines (except for the one that travels out from the midpoint between the two sources) are actually ________________, hyperbolic but their curvature is so slight that we assume them to be linear for most calculations. On either side of the nodal lines are areas of constructive interference (where either two crests or two _____________ and _____________, which areantinode troughs meet). These regions alternate between supercests ________________ supertroughs and create what is called antinodallines _______________________. ACTIVITY: Go to this Wave Interference Simulator and click on the Interference option. Click on the speaker icon to change it to sound waves. Play around with the frequency, amplitude, and separation to see how these affect the wave patterns. Look for nodal/antinodal lines. Click on the particles or both options to see how these longitudinal sound waves of air particles look! You can also try this simulator out at some point if you’d like to see more on interference patterns and nodal lines. If you want to get really crazy, try out this 3D wave simulator! QUESTION: If the interference pattern above was created by two speakers what do you think you would hear if you were standing on one of the nodal lines? 31 SPH3U Name: _________________________________________ APHS U4 - Sound and Waves The Interference of Sound Waves (in 3-D) When a tuning fork vibrates its tines act as two point sources of sound waves and an interference pattern like the one from the ripple tank simulator is formed*. *Actually, the pattern is slightly different because the tines are out of phase… but it’s very similar QUICK ACTIVITY: Grab a tuning fork, lightly hit it on something to get it ringing, and then spin it near your ear to hear areas of constructive and destructive interference. When the sound seems to go away, your ears are in line with a nodal line nodal _________________ and then you are hearing it, your ears are in line with an _________________. I anti line Two speakers in phase can produce an interference pattern exactly like the one from the ripple tank simulator (previous page). The midpoint line in this pattern is an antinoda _____________ line and is the area of greatest sound intensity. Keep in mind that in real life, the nodal lines and antinodal don’t correspond to complete constructive or destructive interference because sound is also reflected off of walls and the ceiling, creating a complex web of spherical sound wave fronts going in all directions (echos and/or reverb). DEMO: Use two speakers about 2 m apart playing the same 500 Hz tone (using this tone generator). Quietly and carefully, walk back and forth in the room and carefully listen for nodal lines. Note that it is possible that this does not work at all because of what was mentioned earlier about the reflection of sound waves creating echoes and reverberation. Noise cancellation headphones use digitally created waves that are perfectly out of phase with ambient sound waves to completely cancel them out. Understanding Concepts 1. Explain in your own words why there are loud and soft intensities in the area around a tuning fork. 2. Stereo speakers have colour-coded terminals (usually black and red) in the back that are hooked up to the wire from the amplifier in the stereo system. If the connections are reversed, the second speaker moves out when the first speaker moves in. Why is it important to wire both speakers so they move in and out together? 3. Distinguish between destructive and constructive interference. 4. Theatres and concert halls are designed to eliminate “dead spots”. Research the answers to the following questions. a. What are “dead spots”? b. How do engineers eliminate the “dead spots” from these facilities? 32 SPH3U Name: _________________________________________ APHS U4 - Sound and Waves Beat Frequency When two different frequencies that are very close to each other are played at the same time, a strange phenomenon occurs where the areas of compression and rarefaction sync up only once in a while. The resulting sound seems to fluctuate between high intensity (loud) to low intensity (quiet). These periodic beat changes in sound intensity that we hear are each called a _____________. beat The number of maximum intensity points (beats) that occur per second is called the ______________________, frequency and it can be determined using the following formula: feat f fat The figure below on the right shows the resulting waveform when a 16 Hz source is played at the same time 2 as a 14 Hz source. This produces a beat frequency of _____ Hz. DEMO: Try out this beat simulator with different pairs of frequencies. Use a stopwatch to confirm the number of beats per second. Try to find the threshold between when we are able to hear distinct beats and when we just hear two different tones. It’s also kind of cool to try and make different chords. Check the reduced fractions to see if they are “nice” fractions or not (remember that this helps determine consonance and dissonance). DEMO: Here is a visual beat simulator that actually shows the frequencies as transverse waves. This may help you to visualise where the beats are occurring by showing the wave that is the sum of the other two. Example 1: A 256 Hz tuning fork is played at the same time as a piano note. 9 beats are heard in 3 seconds. What note is being played on the piano? Frat l fi fi fheat 3 1256 fal 2599Hz E 256 13 **Homework on next page** 253Hz 3Hz 33  SPH3U Name: _________________________________________ APHS U4 - Sound and Waves Homework: 1. You sound two tuning forks together. One has a frequency of 300 Hz, the other a frequency of 302 Hz. What do you hear? beats second 2 per 2. When a tuning fork with a frequency of 256 Hz is sounded at the same time as a second tuning fork, 20 beats are heard in 4.0 s. What are the possible frequencies of the second fork? Hz 2764202 3. What is the beat frequency when a 512 Hz and a 514 Hz tuning fork are sounded together? 4. Two tuning forks are sounded together. One tuning fork has a frequency of 200 Hz. An observer hears 21 beats in 3.0 s. What are the possible frequencies of the other tuning fork? 5. State the beat frequency when the following pairs of frequencies are heard together: 207 193Hz a. 202 Hz, 200 Hz b. 341 Hz, 347 Hz c. 1003 Hz, 998 Hz 9124 b GHz c SHE 6. Use the principle of superposition to “add” these two sound waves together on a piece of graph paper turned sideways a. Wave A: λ = 4.0 cm; A= 1.0 cm; 5 wavelengths b. Wave B: λ = 5.0 cm; A = 1.0 cm; 4 wavelengths c. Describe how the resulting pattern relates to the production of beats 7. A tuning fork with a frequency of 4.0 x 102 Hz is struck with a second tuning fork, and 20 beats are counted in 5.0 s. What are the possible frequencies of the second fork? 40447439GHz 8. A third fork with a frequency of 410 Hz is struck with the second fork from the above question, and 18 beats are counted in 3.0 s. What is the frequency of the second fork? 04th 9. A 440 Hz tuning fork is sounded together with a guitar string, and a beat frequency of 3 Hz is heard. ship When may an elastic band is wrapped tightly around one prong of the tuning fork, a new beat frequency of 2 Hz is heard. Determine the frequency of the guitar string. 34