Physics Lecture: Waves and Sound PDF

# Physics ## Chapter (2) ### Waves and Sound Dr. Mohamed EL-Henawey PhD, Physics Department, Faculty of Science Mansoura University ## Traveling Waves: - A wave is a disturbance that moves through matter or space, usually transfers the energy from one place to another. ### Types of waves - **Mec...

# Physics ## Chapter (2) ### Waves and Sound Dr. Mohamed EL-Henawey PhD, Physics Department, Faculty of Science Mansoura University ## Traveling Waves: - A wave is a disturbance that moves through matter or space, usually transfers the energy from one place to another. ### Types of waves - **Mechanical:** which require material medium for their Propagation - **Transverse Waves** - **Longitudinal waves** - **Electromagnetic:** which does not require material medium for their Propagation ## Properties of waves: - **Wavelength (λ):** is the distance between one point on a wave and the nearest point moving with the same speed and direction. - **Frequency (ν):** is the number of wavelengths that pass by a point each second. - **Periodic time (T):** the time taken for one complete cycle of vibration to pass a given point. **Wave speed (m/s) = Wavelength (m) x Frequency (Hz)** **V = λχν** **Frequency v = 1/T** **Speed V = λ/T** ## Traveling waves: - One of the easiest ways to produce a simple wave motion is by vibrating the end of a long string. - It is found that V depends upon the density ρ, the cross sectional area A of the string, and the tension T in the string, that is **V = √(T/ρA)** ### 1. Transverse Wave: It is the wave in which the molecules of the medium move (or vibrate) in a direction perpendicular to the direction of propagation of the wave. These waves can be propagated through solids. ### 2. Longitudinal Wave: It is the wave in which the molecules of the medium move (or vibrate) along the direction of wave motion. These waves propagate through gases, liquids, and solids. ## Standing Waves: ### Superposition: The combination of wave pulses is one example of the phenomenon of interference. When the pulses added together, we say that the interference is constructive. When the pulses cancel each others, we say that the interference is destructive. ### Reflection of wave pulses: Consider a string that is terminated at one end (attached to a rigid wall). Suppose that we send a wave pulse along the terminated string. When the pulse reaches the terminated end, the pulse will be reflected and will proceed back along the string in the opposite direction. The reflected wave pulse has the same size and shape as the initial pulse, ## Standing Waves: But the sign of the displacement is reversed. The reflected wave and the incoming wave interfere with each other. at the reflecting surface, the two waves are always exactly equal and opposite - so they always cancel out. Such a place is called a NODE. At other points along the waves, the two ways always are the same - so they add together or interfere constructively and make a double size wave. Such points are called ANTINODES. - A - places where the waves interfere constructively and make double height wave - ANTINODE. - N - places where the two waves always 'cancel' out so there is no movement- NODE. - The distance between two NODES or between two ANTINODES is half a wavelength. ## Standing Waves: Such waves are called Standing Waves - The relation between the wave length λ and the string length Lis **L = nλ/2** **λ = 2L/n , n=1,2,3,...** ## Standing Waves: - L - 1st harmonic - 2nd harmonic - 3rd harmonic - 4th harmonic - n | name | L = nλ/2 | Wavelength λ = 2L/n | Frequency (ν=V/λ) ------- | -------- | -------- | -------- | -------- 1 | Fundamental (or 1st harmonic) | L = λ/2 | λ = L | νo = V/2L 2 | 1st overtone (or 2nd harmonic) | L = 2λ/2 | λ = L/2 | ν1 = V/L = 2νo 3 | 2nd overtone (or 3rd harmonic) | L = 3λ/2 | λ = 2L/3 | ν2 = 3V/2L = 3νo 4 | 3rd overtone (or 4th harmonic) | L = 4λ/2 | λ = L/4 | ν3 = 2V/L = 4νo ## Sound Waves: - Compressional waves that are due to a vibrating source and that are capable of producing assignation in the auditory system are called Sound waves. - The human ear is responsive to the sound waves if they have frequencies in the range from 15 Hz to about 20,000 Hz. - The velocity of sound in air is 330 m/s at 0°C. - The velocity of the sound V depends on the elastic properties of the medium - In fluids, the speed can be reorganize in terms of the Bulk modulus B and density ρ **V = √(B/ρ)** - In solids, the sound speed depends on the Young's modulus, Y, **V = √(Y/ρ)** ## The vibration of air in pipes: - When we place a fork above the open end of the pipe, the air at the closed end is not free to vibrate so a node is formed at the closed end. While the air at the open end is free to vibrate with maximum amplitude so an antinode is formed at this end. This is the simplest mode of vibration and is called fundamental mode. - The shortest air column for which the resonance is occurs has a length of **L = λ/4 or λ = 4L** The frequency **ν = V/λ = V/4L** ## The vibration of air in pipes: - In general, the resonance occurs in a closed air column when the wavelength is given by **L = nλ/4 & λ = 4L/n** The corresponding frequency is given by **ν = V/λ = nV/4L** - n | name | λ= 4L/n | ν ------- | -------- | -------- | -------- 1 | Fundamental (or 1st harmonic) | λ = 4/1 L | νo = V/4L 3 | 1st overtone (or 2nd harmonic) | λ = 4/3 L | ν1 = 3V/4L 5 | 2nd overtone (or 3rd harmonic) | λ = 4/5 L | ν2 = 5V/4L ## Doppler effect: - The Doppler effect: Doppler Effect refers to the change in wave frequency during the relative motion between a wave source and its observer. - For example, when a sound object moves towards you, the frequency of the sound waves increases, leading to a higher pitch. Conversely, if it moves away from you, the frequency of the sound waves decreases and the pitch comes down. The drop in pitch of ambulance sirens as they pass by and the shift in red light are common examples of the Doppler Effect. ## Doppler effect: - The frequency as determined by listener is: ** VL = Vs/(1-Vs/V) (Source moving toward listener)** **VL = Vs/(1+Vs/V) (Source moving away from listener)** - VL: frequency as determined by listener. - Vs: frequency of the waves. - V: the velocity of the waves in the medium. - Vs: the velocity of the source. - Doppler effect applies to all types of wave motion, water, sound, light, and electromagnetic radiation. - Doppler radar, is used to identify motor vehicles that are exceeding the speed limit. ## Examples: - Example (1): What is the frequency of the first overtone that can be heard from an organ pipe that is closed at one end and has a length of 2.5 m if the temperature of the air is 20° C. assume that the speed of sound in air at this temperature is 344 m/s? Solution: - For a pipe closed at one end, the first overtone corresponding to the third harmonic which mean that n=3. **ν = nV/4L = (3 x 344 m/s)/(4 x 2.5 m) = 103 Hz** - Example (2): An airplane is flying at Mach 0.5 (half the speed of sound) and carries a sound source that emits a 1000 Hz single. What frequency sound does a listener hear if he is in the path of the airplane? Solution: ** Mach = (Speed of body)/(Speed of sound in the surrounding medium) = Vs/V = 0.5** - listener is in the path of the airplane so, **VL = Vs/(1-Vs/V) , So, VL = 1000/(1-0.5) = 2000 Hz** - What is the frequency does the listener hear after the airplane has passes? ** VL = Vs/(1+Vs/V) So, VL = 1000/(1+0.5) = 666.6 Hz** ## Bioscience Essay (Ear and Hearing): ### Ear and Hearing: - The human ear is one of the most marvelous devices constructed for sensing information carried by waves. The human ear consist of: 1. **The outer ear:** consist of the ear canal which is a kind of closed and acoustic pipe. At the end of the ear canal is the tympanic membrane (ear drum) 2. **The middle ear:** consist of small bones, these bones are named according to their shapes: the malleus (hummer), incus and the stapes . ### Middle Ear Function: A. **Impedance Matching:** amplification of sounds to overcome difference in impedance between the air of the outer ear and the fluid ofresonant frequency is approximately 1000 Hz, functions as bandpass filter the inner ear, to improves" the transmission of sound from the outer ear to the inner ear. B. **Filtering:** - resonant frequency is approximately 1000 Hz, functions as bandpass filter. C. **Acoustic Reflex:** - Contraction. of Stapedius muscle in response to loud sounds. - **Impedance Matching:** is accomplished through pressure increase produced by the middle ear, From 2 main effects: A. **Reduction in Area:** - Sound striking the (relatively large) tympanic membrane. - Is delivered to the (much smaller) stapes footplate. - Areal Ratio = 18.6 to 1. B. **Increase in Force:** - The malleus and incus act like a lever, whenever there is a pivot: - **Force x Length in = Force x Length out.** - Force is greater on short side (Think of wheeled luggage). - Malleus manubrium = 1.3 times as long as Incus long process. 2. **The inner ear** or Cochlea, the inner ear is mainly responsible for **sound detection** and **balance**. ## How can we hear with the ear? - Sound waves entre the system through the ear canal. - The air column in ear canal will resonate for a sound wavelength equal to 4 times its length (λ = 4L). - The pressure variations of the incident sound wave are transmitted by ear drum to the bones in the middle ear. - The bones serve to match the response of the outer ear to that of the inner ear (cochlea). - The vibratory motion of the stapes is transmitted to the cochlear fluid through the oval window. - The sound energy that passage through the fluid in the ducts in cochlea sets into motion the basilar membrane which in turn, excites the cells of the hairline fibers that are connected to the end organ of the auditory nerve. - The electrical signals that are generated are transmitted to the brain and the sensation of hearing results.