Grade 11 Physics Midyear Exam PDF

Grade 11 Physics study-guide Midyear exam The upcoming final exam for Physics will take place on Wednesday, 11 December 2024. The paper has a total mark of 30, with the following sections: Section1: Multiple-choice questions (MCQ) – 20 questions worth 1 mark each Section 2: Longer questi...

Grade 11 Physics study-guide Midyear exam The upcoming final exam for Physics will take place on Wednesday, 11 December 2024. The paper has a total mark of 30, with the following sections: Section1: Multiple-choice questions (MCQ) – 20 questions worth 1 mark each Section 2: Longer questions (calculations + writing) – 5 questions worth 10 marks in total. The exam will cover the following topics: 1) Waves Hooke’s Law Simple pendulum Characteristics of waves Types of waves & Speed of waves Interference 2) Sound Characteristics of sound waves Doppler effect Standing waves and harmonics 3) Light Electromagnetic waves Reflection off a plane mirror Resources: This study guide will help you to study for the exam by covering all the work you need to know for the exam. Additional resources will be uploaded on Toddle. Formula sheet: A formula sheet will be provided in the exam paper. The next page shows an exact copy of the formula sheet you will get in the exam. Remember to use the correct SI units in your calculations. A list is provided below: o 𝑓 = 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 (𝐻𝑧) o 𝑇 = 𝑝𝑒𝑟𝑖𝑜𝑑 (𝑠) o 𝜆 = 𝑤𝑎𝑣𝑒𝑙𝑒𝑛𝑔𝑡ℎ (𝑚) o 𝐹 = 𝑓𝑜𝑟𝑐𝑒 (𝑁) o 𝑘 = 𝑠𝑝𝑟𝑖𝑛𝑔 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 (𝑁/𝑚) o 𝑃𝐸 = 𝑝𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 𝑒𝑛𝑒𝑟𝑔𝑦 (𝐽) o 𝑥 = 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 (𝑚) o 𝐿 = 𝑙𝑒𝑛𝑔𝑡ℎ (𝑚) o 𝑣 = 𝑠𝑝𝑒𝑒𝑑 (𝑚/𝑠) o 𝑐 = 𝑠𝑝𝑒𝑒𝑑 𝑜𝑓 𝑙𝑖𝑔ℎ𝑡 (𝑚/𝑠) Emirates National Schools- Al Ain AY 2024-2025 1  Fundamental Constants Metric (SI) multipliers Quantity Symbol Value Acceleration of free fall gravity 𝒂𝒈 𝟗. 𝟖𝟏 𝒎/𝒔𝟐 ( Earth’s surface) Speed of light 𝒄 𝟑. 𝟎 × 𝟏𝟎𝟖 𝒎/𝒔 Formula Sheet: 𝟏 𝟏 𝒇= 𝑻= 𝑻 𝒇 𝑳 𝑻𝟐. 𝒂𝒈 𝑻 = 𝟐𝝅√ 𝑳= 𝒂𝒈 𝟒𝝅𝟐 𝟏 𝟐 𝑭𝒔𝒑𝒓𝒊𝒏𝒈 = −𝒌𝒙 𝑷𝑬𝒆𝒍𝒂𝒔𝒕𝒊𝒄 = 𝒌𝒙 𝟐 𝒗=𝒇×𝝀 𝒄= 𝒇×𝝀 𝒗 ± 𝒗𝒐 𝟐𝑳 𝒇′ = 𝒇 ( ) 𝝀𝒏 = 𝒗 ± 𝒗𝒔 𝒏 𝒏. 𝒗 𝒏. 𝒗 𝒇𝒏 = 𝒇𝒏 = 𝟐𝑳 𝟒𝑳 Emirates National Schools- Al Ain AY 2024-2025 2 WAVES Review notes Characteristics of Waves: Graph 1 Graph 2 The wavelength of a wave is The amplitude of a wave is the The period (T) of a wave is the length it takes to complete maximum vertical movement of the time needed for one full one wave motion, for example the wave from its resting position cycle of the motion (wave) to crest to crest. The symbol for (equilibrium). Amplitude is be completed. Period is wavelength is λ (lambda) and it measured in meter (m) and is measured in seconds (s), is measured in meter (m). It is read from the vertical axis on from the horizontal axis of a read on the horizontal axis of the the graph. Both graph 1 and 2 time graph, like graph 2. graph, if x-axis shows length, shows distance on the y-axis. like in graph 1 The frequency (f) of a wave is the number of wavelengths that pass a given point in a The frequency (f) and period (T) of a wave are certain amount of time (1 sec). reciprocals of one another. This means: Frequency is measured in hertz (Hz). 𝟏 𝟏 𝒇= & 𝑻= 𝑻 𝒇 𝟏 𝟏 For example, if T = 4s, then 𝒇 = 𝑻 = 𝟒 = 𝟎. 𝟐𝟓 𝑯𝒛 The energy of a wave is directly related to its amplitude and its frequency: The greater the amplitude of a wave, the more energy it has. For example, if the height of a sound wave increases, each wave will have more energy (and the sound will be louder). The greater the frequency of a wave, the more energy it has. For example, if you move the end of a jump rope up and down, a wave is produced. To increase the frequency, you have to move the rope more rapidly, which requires you to exert more energy. Examples: Multiple Choice Questions 1. The time that it takes a wave to complete one cycle is known as … (1pt) a. amplitude b. period c. frequency d. herz Emirates National Schools- Al Ain AY 2024-2025 3  Answer questions 2, 3 and 4 using the diagram shown below: 2. In the diagram above, the wave has a period of … (1pt) a. 1s b. 2s c. 4s d. 6s 3. In the diagram above, the wave’s amplitude is … (1pt) a. 0 cm b. 1 cm c. 2 cm d. 4 cm 4. In the diagram above, the wave’s frequency is … (1pt) a. 0.25 Hz b. 2 Hz c. 4 Hz d. 6 Hz 5. Frequency and period are reciprocals of one another. If it is given that a certain wave has a frequency of 10.0 Hz, calculate the period of the wave. (1pt) a. 10.0 s b. 0.1 s c. 1.0 s d. 0.01 s 6. The amplitude of a mechanical wave determines how much ________________ the wave transfers per unit time. a. material b. wavelengths c. particles d. energy 7. What can you infer about a wave with a short wavelength? (1pt) a. It has a low frequency. b. It has a high frequency. c. It has a low amplitude. d. It has a high amplitude. Emirates National Schools- Al Ain AY 2024-2025 4  8. What does it mean when a wave's amplitude increases? (1pt) a. Its frequency also increases. b. Its wavelength gets longer. c. Its energy also increases. d. Its period also increases. 9. The picture alongside shows waves created by shaking a rope up and down. The waves are not reflected by the wall.Which one of the following statements is correct? The wave’s amplitude is The wave’s wavelength is shown by the letter … shown by the letter … A. X Y B. Z X C. Y X D. X Z 10. The unit for frequency is defined as “cycles per second” and is called … A. lambda (λ) B. hertz (Hz) C. meter (m) D. newton (N) Answer questions 11 and 12 by finding the answer in the correct one of the two graphs given below: Graph 1 Graph 2 cm cm 11. The correct number value of the wavelength from the appropriate graph is ____ A. 4 B. 5 C. 10 D. 12 12. The correct number value of the period from the appropriate graph is ____ A. 4 B. 5 C. 10 D. 12 Emirates National Schools- Al Ain AY 2024-2025 5  13. In the diagram alongside, which wave pattern has the highest frequency? A. Wave pattern 1 B. Wave pattern 2 C. Wave pattern 3 D. Wave pattern 4 Examples calculation type questions: 1. A wave traveling in the positive x direction with a frequency of 25.0 Hz is shown in the figure below. Determine the following values for this wave: a. Amplitude (1pt) ____18 ÷ 2 = 9 cm_________________________________________________ b. Wavelength (1pt) _____10 × 2 = 20 cm______________________________________________ c. Period (2pts) 𝟏 𝟏 _____𝑻 = 𝒇 = 𝟐𝟓 = 𝟎. 𝟎𝟒 𝒔__________________________________________ 12. Graph 1 below shows the variation with time t of the displacement d of a traveling wave. Graph 2 below shows the variation with distance x along the same wave of its displacement d. (6pts) a. Use the graphs to determine the amplitude of the wave motion. ______4 mm______________________________ ________________________________________ b. Use the graphs to determine the wavelength. ______2.4 cm_____________________________ ________________________________________ c. Use the graphs to determine the period. ____0.3 s_________________________________ ________________________________________ d. Determine the frequency of the wave in Graph 1. 𝟏 𝟏 ____ 𝑻 = 𝒇 = 𝟎.𝟑 = 𝟑. 𝟑 𝒔 ________________________ Emirates National Schools- Al Ain AY 2024-2025 6  Hooke’s Law: Measurements show that the spring force is directly proportional to the displacement of the mass. This relationship is known as Hooke’s Law: Felastic = –kx spring force = – (spring constant  displacement) The quantity k is a positive constant called the spring constant. It basically describes the stiffness of the spring and it is measured in newton/meter (N/m). The value x describes the distance that the spring is stretched from its equilibrium position. If the spring is compressed up, displacement is + x. If the spring is stretched downward, displacement is – x. Potential Energy in a Spring When a spring is stretched, energy is transferred to it, giving it elastic potential energy (PEspring) 𝟏 To calculate this energy, use the formula: 𝑷𝑬𝒔𝒑𝒓𝒊𝒏𝒈 = 𝒌𝒙𝟐 𝟐 Examples multiple choice questions: 1. A net force of 120 N acts to stretch an extension spring. How far will the spring stretch downward if its spring constant is 240 N/m? A. 2.0 m B. 28 800 m C. 360 m D. 0.5 m 2. A net force of 80 N acts to stretch an extension spring. How far will the spring stretch downward if its spring constant is 320 N/m? A. 4.0 m B. 0.25 m C. 25 600 m D. 400 m Examples calculation type questions: 1. A spring stretches by 0.18 m when a bag of potatoes weighing 56 N is suspended from its end. a. Determine the spring constant (k). 𝑭 = −𝒌𝒙 𝟓𝟔 = −𝒌(−𝟎. 𝟏𝟖) 𝟓𝟔 𝒌(𝟎. 𝟏𝟖) = 𝟎. 𝟏𝟖 𝟎. 𝟏𝟖 𝒌 = 𝟑𝟏𝟏. 𝟏 ≈ 𝟑𝟏𝟎 𝑵/𝒎 b. How much elastic potential energy does the stretched spring have? 𝟏 𝑷𝑬 = 𝒌𝒙𝟐 𝟐 𝟏 𝑷𝑬 = (𝟑𝟏𝟎)(−𝟎. 𝟏𝟖)𝟐 𝟐 𝑷𝑬 = 𝟓. 𝟎 𝑱 Emirates National Schools- Al Ain AY 2024-2025 7  2. What is the spring constant of a spring that stretches 12 cm when a 20 N object is hung from it? 𝑭 = −𝒌𝒙 𝒙 = −𝟏𝟐 𝒄𝒎 ÷ 𝟏𝟎𝟎 = −𝟎. 𝟏𝟐 𝒎 𝟐𝟎 = −𝒌(−𝟎. 𝟏𝟐) 𝟐𝟎 𝒌(𝟎. 𝟏𝟐) = 𝟎. 𝟏𝟐 𝟎. 𝟏𝟐 𝒌 = 𝟏𝟔𝟔. 𝟕 ≈ 𝟏𝟕𝟎 𝑵/𝒎 3. What is the elastic potential energy of a spring with k = 144 N/m that is compressed by 16.5 cm? 𝟏 𝑷𝑬 = 𝟐 𝒌𝒙𝟐 𝒙 = 𝟏𝟔. 𝟓 𝒄𝒎 ÷ 𝟏𝟎𝟎 = 𝟎. 𝟏𝟔𝟓 𝒎 𝟏 𝑷𝑬 = (𝟏𝟒𝟒)(𝟎. 𝟏𝟔𝟓)𝟐 𝟐 𝑷𝑬 = 𝟐. 𝟎 𝑱 Simple pendulum: A simple pendulum consists of a mass (called a bob), which is attached to a fixed string or rod of length L. The bob swings back and forth as shown in the figure. The period (T) of a simple pendulum depends on L (length of the string or rod) and on g (the free-fall acceleration or gravity on the bob). The following formula can be used: 𝑳 𝑙𝑒𝑛𝑔𝑡ℎ 𝑻 = 𝟐𝝅√ 𝑝𝑒𝑟𝑖𝑜𝑑 = 2𝜋√ 𝒈 𝑔𝑟𝑎𝑣𝑖𝑡𝑦 Note that period does not depend on the mass of the bob or the amplitude, but only the length of the pendulum. The longer the pendulum is, the larger the period will be. Shorter pendulums will have shorter periods. Note: The simple pendulum’s period formula can be changed to calculate length as well: 𝑻𝟐 𝒈 Length: 𝑳 = 𝟒𝝅𝟐 Examples multiple choice questions: 1. Which pendulum will have the longest period? Pendulum A: a 1 kg mass attached to a 1.5 m long string, or Pendulum B: a 1 kg mass attached to a 1.0 m long string A. Pendulum A B. Pendulum B C. Both will have the same period. D. It is impossible to determine with the information given. Emirates National Schools- Al Ain AY 2024-2025 8  2. Which pendulum will have the longest period? Pendulum A: a 2 kg mass attached to a 0.8 m long string Pendulum B: a 4 kg mass attached to a 0.8 m long string A. Pendulum A B. Pendulum B C. Both will have the same period. D. It is impossible to determine with the information given. Examples calculation type questions: 1. A pendulum has a length of exactly 1.0 m. a. What is the period of this pendulum on Earth, where g = 9.81 m/s2? 𝑳 𝟏. 𝟎 𝑻 = 𝟐𝝅√ = 𝟐𝝅√ = 𝟐. 𝟎 𝒔 𝒈 𝟗. 𝟖𝟏 b. Determine the frequency of this same pendulum. 𝟏 𝟏 𝒇= = = 𝟎. 𝟓 𝑯𝒛 𝑻 𝟐. 𝟎 2. A trapeze artist at a circus swings in simple harmonic motion with a period of 3.8 s. Calculate the length of the cables supporting the trapeze. 𝑻𝟐 𝒈 (𝟑. 𝟖)𝟐 (𝟗. 𝟖𝟏) 𝑳= = = 𝟑. 𝟔 𝒎 𝟒𝝅𝟐 𝟒𝝅𝟐 Types of waves & Wave speed: Waves that require a medium through which to travel are called mechanical waves. Water waves and sound waves are mechanical waves. Electromagnetic waves such as visible light do not require a medium. Transverse wave vs. Longitudinal wave: A transverse wave is a wave whose particles vibrate perpendicularly to the direction of the wave motion. A longitudinal wave is a wave whose particles vibrate parallel to the direction the wave is traveling. A longitudinal wave on a spring at some instant t can be represented by a graph. The crests correspond to compressed regions called compressions, and the troughs correspond to stretched regions, called rarefactions. Emirates National Schools- Al Ain AY 2024-2025 9  Wave speed: The speed of a mechanical wave is constant for any given medium. The speed of a wave is given by the following equation: 𝒗=𝒇×𝝀 wave speed = frequency  wavelength This equation applies to both mechanical and electromagnetic waves. Examples multiple choice questions: 1. The image shows a student using a Slinky to create a wave. The slinky is stretched at one end and the resulting wave travels back and forth. This is an example of a... A. Transverse wave B. Superposition wave C. Longitudinal wave D. Electromagnetic wave 2. A mechanical wave cannot travel through... A. Air B. Water C. Solids D. Empty space (vacuum). 3. Which part of this wave type shown is where particles are packed closely together? A. Crest B. Rarefaction C. Compression D. Amplitude 4. What types of waves carry energy at a right angle or perpendicular to the direction of the energy flow? A. Transverse wave B. Superposition wave C. Longitudinal wave D. Electromagnetic wave Emirates National Schools- Al Ain AY 2024-2025 10  Examples calculation type questions: 1. A wave with a frequency of 14 Hz has a wavelength of 3 meters. At what speed will this wave travel? 𝒗 = 𝒇 × 𝝀 = 𝟏𝟒 × 𝟑 = 𝟒𝟐 𝒎/𝒔 2. The speed of a wave is 65 m/s. If the wavelength of the wave is 0.8 meters, what is the frequency of the wave? 𝒗 𝟔𝟓 𝒇= = = 𝟖𝟏. 𝟐𝟓 𝑯𝒛 𝝀 𝟎. 𝟖 3. The red light emitted by a He-Ne laser has a wavelength of 633 nm in air and travels at 3.00 × 10 8 m/s. Find the frequency of the laser light. 𝒗 𝟑. 𝟎𝟎 × 𝟏𝟎𝟖 𝒇= = = 𝟒. 𝟕𝟒 × 𝟏𝟎𝟏𝟒 𝑯𝒛 𝝀 𝟔𝟑𝟑 × 𝟏𝟎−𝟗 4. A wave with a frequency of 0.5 MHz is traveling at a speed of 200 m/s. What is the wavelength? 𝒗 𝟐𝟎𝟎 𝝀= = = 𝟒 × 𝟏𝟎−𝟒 𝒎 𝒇 𝟎. 𝟓 × 𝟏𝟎𝟔 Interference Reflection of waves: When a wave (or wave pulse) meets a solid boundary between 2 different mediums, the wave will be reflected. As shown in the picture, the wave that travels toward the boundary is called the incident wave, and after it hits the boundary, the wave is called the reflected wave. There are 2 types of reflection of waves: 1. When reflection is off a fixed boundary (where the rope is tied tight to the boundary and cannot move up or down), the wave is both reflected and inverted (upside down). 2. When reflection is off a free boundary (where the rope can move up and down the boundary because it is loose around it), the wave is only reflected and will stay upright. Emirates National Schools- Al Ain AY 2024-2025 11  Interference of waves: Interference is a phenomenon in which two waves superpose to form a resultant wave of greater, lower, or the same amplitude. There are 2 types of interference: 1. Constructive interference, where individual displacements on the same side of the equilibrium position (in phase) are added together to form the resultant wave. 2. Destructive interference, where the individual displacements on opposite sides of the equilibrium position (out of phase) are subtracted to form the resultant wave. Examples multiple choice questions: 1. Which of the following types of interference will occur when the pulses in the figure above meet? a. no interference c. destructive interference b. constructive interference d. total interference 2. Two waves meet and interfere constructively. Which one of the following factors increase? a. amplitude c. wavelength b. period d. frequency 3. The diagram shows two pulse waves with the same amplitudes moving toward each other through a medium. The two waves will exactly superpose when they reach point A. At point A, the amplitude of the combined waves will be … a. twice the amplitude of either wave alone. b. the same as either wave alone. A c. zero d. half that of either wave alone 4. The type of wave interference described in question 3 is best described as … a. superposition c. reflection b. constructive interference d. destructive interference 5. Incident waves arriving at a free boundary are: a. neither reflected nor inverted. c. reflected and inverted. b. reflected but not inverted. d. inverted but not reflected. 6. A rope is fixed tightly to a wall and a single incident wave pulse is sent down the rope. The pulse is reflected from this fixed boundary. How will this reflected wave look like? a. neither reflected nor inverted. c. reflected and inverted. b. reflected but not inverted. d. inverted but not reflected. Emirates National Schools- Al Ain AY 2024-2025 12 7. Two wave pulses travel toward each other as shown in the diagram. Pulse (a) has an amplitude of 15 mm and pulse (b) has an amplitude of 25 mm. At the exact moment that the pulses superpose, what will be the amplitude of the combined pulses? a. 40 mm c. 32.5 mm b. 10 mm d. –10 mm Examples calculation type questions: 1. A string is rigidly attached to a post at one end. Several pulses of amplitude 0.15 m sent down the string are reflected at the post and travel back down the string without a loss of amplitude. a. What is the amplitude at a point on the string where the maximum displacement points of two pulses cross? What type of interference is this? 𝟎. 𝟏𝟓 − 𝟎. 𝟏𝟓 = 𝟎 𝒎 Destructive interference b. How would your answer to a) change if the same pulses were sent down a string whose end is free? What type of interference is this? 𝟎. 𝟏𝟓 + 𝟎. 𝟏𝟓 = 𝟎. 𝟑𝟎 𝒎 Constructive interference Emirates National Schools- Al Ain AY 2024-2025 13  SOUND Review notes Characteristics of Sound: All sound waves are mechanical waves that must have a medium to travel Sound waves are longitudinal. The simplest longitudinal wave produced by a vibrating object can be represented by a sine curve. In the diagram, the crests of the sine curve correspond to compressions, and the troughs correspond to rarefactions. The frequency of an audible sound wave determines how high or low we perceive the sound to be, which is known as pitch. As the frequency of a sound wave increases, the pitch rises. How loud a sound is depend mostly on the amplitude of the pressure wave. Louder sounds will have larger amplitudes, and vice versa. Examples multiple choice questions: 1. The image shows 4 different sound waves travelling at the same speed in air over a period of 2 seconds. Which wave has the lowest pitch? A. Wave 1 B. Wave 2 C. Wave 3 D. Wave 4 2. The image shows 2 different sound waves travelling at the same speed Wave A in air over a period of 2 seconds. Which wave shows the loudest sound? A. Wave A B. Wave B C. They have the same loudness but different pitches. Wave B Examples calculation type questions: 3. The more energy that a sound has, the louder the sound will become. Look at the following two waves. Which wave represents the volume of the sound becoming louder? Give a reason for your answer. (2 marks) Wave B is getting louder. The amplitude of the wave increases over time. Emirates National Schools- Al Ain AY 2024-2025 14  Doppler effect: The Doppler effect is the observable change in frequency of a sound when there is relative motion between the source of the sound and an observer Because frequency determines pitch, the Doppler effect affects the pitch heard by each listener. The formula to determine the frequency an observer hear (f ’) is: 𝑣𝑠𝑜𝑢𝑛𝑑 ± 𝑣𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑟 𝒗 ± 𝒗𝒐 𝒇′ = 𝑓 ( ) = 𝒇( ) 𝑣𝑠𝑜𝑢𝑛𝑑 ± 𝑣𝑠𝑜𝑢𝑟𝑐𝑒 𝒗 ± 𝒗𝒔 where: f’ = frequency heard f = original frequency v = vsound = speed of sound in a medium vo = vobserver = speed of observer vs = vsource = speed of source To decide on which formula to use, see the following table: at rest Observer moves … towards source away from source (vo = 0) 𝑣𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑟 𝑣 + 𝑣𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑟 𝑣 − 𝑣𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑟 𝑣 At rest Source moves Towards observer Away from observer (vs = 0) 𝑣𝑠𝑜𝑢𝑟𝑐𝑒 𝑣 − 𝑣𝑠𝑜𝑢𝑟𝑐𝑒 𝑣 + 𝑣𝑠𝑜𝑢𝑟𝑐𝑒 𝑣 Examples multiple choice questions: 1. In which one of the following cases will the Doppler effect not be observed? A. A source of sound moves toward a listener. B. A listener moves toward a source of sound. C. A listener and a source of sound move toward or away from each other. D. A listener and a source of sound remain at rest with respect to each other. 2. The horn of a parked automobile is stuck. If you are in a vehicle that passes the automobile, as shown in the diagram, what is the nature of the sound that you hear? A. The original sound of the horn rises in pitch B. The original sound of the horn drops in pitch. C. A higher pitch is heard dropping to a lower pitch. D. A lower pitch is heard rising to a higher pitch. Emirates National Schools- Al Ain AY 2024-2025 15  Examples calculation type questions: 3. A car is moving at 24.6 m/s towards a man who is standing still. The car is playing loud music at a frequency of 523 Hz. What frequency will the man hear as the car travels toward him? (Assume the speed of sound in air is 343 m/s) 𝒗 𝟑𝟒𝟑 𝒇′ = 𝒇 ( ) = 𝟓𝟐𝟑 ( ) = 𝟓𝟔𝟑 𝑯𝒛 𝒗 − 𝒗𝒔 𝟑𝟒𝟑 − 𝟐𝟒. 𝟔 4. You are in a car driving at a speed of 25.0 m/s towards a pole-mounted siren. If the siren’s frequency is 365 Hz, what frequency do you hear? (Speed of sound in air = 343 m/s) 𝒗+𝒗𝟎 𝟑𝟒𝟑+𝟐𝟓.𝟎 𝒇′ = 𝒇 ( 𝒗 ) = 𝟑𝟔𝟓 ( 𝟑𝟒𝟑 ) = 𝟑𝟗𝟐 𝑯𝒛 5. You are in a car traveling at 22.0 m/s. A second car is moving toward you at the same speed. Its horn is sounding at 475 Hz. What frequency do you hear? Use 343 m/s as the speed of sound in air. 𝒗 + 𝒗𝒐 𝟑𝟒𝟑 + 𝟐𝟐. 𝟎 𝒇′ = 𝒇 ( ) = 𝟒𝟕𝟓 ( ) = 𝟓𝟒𝟎 𝑯𝒛 𝒗 − 𝒗𝒐 𝟑𝟒𝟑 − 𝟐𝟐. 𝟎 Standing waves: A standing wave is a wave pattern that results when two waves of the same frequency, wavelength, and amplitude travel in opposite directions and interfere. The standing wave consists of alternating regions of constructive and destructive interference. As shown in the picture, the points on the standing wave at which complete destructive interference occurs, are called nodes. At each node, the amplitude of the superposed waves is zero. Halfway between two adjacent nodes, the waves interfere at maximum amplitude, and these are called antinodes. Only certain frequencies, and therefore wavelengths, produce standing wave patterns. The wavelength of these standing waves depends on the length (L) of the string. Standing waves can only occur for wavelengths where both ends are nodes and the number of half- wavelengths (antinodes) are integers (n = 1 , 2 , 3 , 4 …) The wavelength for a standing wave in a string of length L: 𝟐𝑳 𝝀𝒏 = , where n is an integer 𝒏 Emirates National Schools- Al Ain AY 2024-2025 16  Harmonics: The vibrations on the string of a musical instrument usually consist of many standing waves, each of which has a different wavelength and frequency. 𝟐𝑳 The greatest possible wavelength on a string of length L is 𝝀𝟏 = = 𝟐𝑳 𝟏 The fundamental frequency, which corresponds to this wavelength, is the lowest frequency of vibration: 𝒇𝟏 = 𝒗 𝒗 = 𝝀𝟏 𝟐𝑳 Each integral multiple of the fundamental frequency is called a harmonic. The fundamental frequency is therefore also called the first harmonic. The harmonic series is a series of frequencies that includes the fundamental frequency and integral multiples of the fundamental frequency, therefore also creating the second harmonic, third harmonic, fourth harmonic, etc. as shown in the diagram. To calculate the frequency of the harmonic series, use the following formulas: Harmonics in strings and open-ended Harmonics in pipes with one end closed pipes (n = 1, 2, 3, …): (n = 1, 3, 5, …): 𝒏. 𝒗 𝒏. 𝒗 𝒇𝒏 = 𝒇𝒏 = 𝟒𝑳 𝟐𝑳 Examples multiple choice questions: 1. How many nodes does this standing wave shown alongside have? A. 2 B. 3 C. 6 D. 7 2. How many antinodes does this standing wave shown alongside have? A. 1 B. 2 C. 3 D. 4 3. Which one of the following wavelengths would produce standing waves on a guitar string that is 3.5 m long? A. 3.8 m B. 2.85 m C. 2.33 m D. 4.5 m 𝟐𝑳 𝟐×𝟑.𝟓 𝟐×𝟑.𝟓 𝟐×𝟑.𝟓 𝝀𝒏 = 𝒏 : 𝝀𝟏 = 𝟏 =𝟕 ; 𝝀𝟐 = 𝟐 = 𝟑. 𝟓 ; 𝝀𝟑 = 𝟑 = 𝟐. 𝟑𝟑 Emirates National Schools- Al Ain AY 2024-2025 17 4. A string vibrates with a standing wave that has a wavelength of 1.2 m. The standing wave has the pattern shown alongside. What is the length of the string? A. 4.0 m B. 3.0 m C. 2.4 m D. 1.8 m 𝟐𝑳 𝟐𝑳 𝟐 𝝀𝒏 = ⟹ 𝟏. 𝟐 = ⟹ 𝑳 = 𝟏. 𝟐 ÷ = 𝟏. 𝟖 𝒎 𝒏 𝟑 𝟑 5. Points of maximum amplitude on a standing wave are called … A. Nodes B. Antinodes C. Points of interference 6. Points of zero amplitude on a standing wave are called … A. Nodes B. Antinodes C. Points of interference. 7. Which one of the following wavelengths would NOT produce standing waves on a guitar string that has a length of 1.20 m? A. 0.80 m B. 1.20 m C. 1.50 m D. 2.40 m 𝟐𝑳 𝟐×𝟏.𝟐 𝟐×𝟏.𝟐 𝟐×𝟏.𝟐 𝝀𝒏 = : 𝝀𝟏 = = 𝟐. 𝟒𝟎 ; 𝝀𝟐 = = 𝟏. 𝟐𝟎 ; 𝝀𝟑 = = 𝟎. 𝟖𝟎 𝒏 𝟏 𝟐 𝟑 8. How many wavelengths are there in a string vibrating at its fundamental frequency? A. 1⁄4 B. 1⁄2 C. 1 D. 2 9. A pipe that is closed at one end and open at the other resonates at a fundamental frequency of 240 Hz. The next harmonic frequency at which this pipe will resonate will be … A. 80 Hz B. 120 Hz C. 480 Hz D. 720 Hz 𝒏. 𝒗 𝒇𝒏 = (𝒏 = 𝟏; 𝟑; 𝟓; … ) ⟹ 𝒇𝟏 = 𝟐𝟒𝟎 ⟹ 𝒇𝟑 = 𝟑 × 𝟐𝟒𝟎 = 𝟕𝟐𝟎 𝑯𝒛 𝟒𝑳 10. The second harmonic of a guitar string has a frequency of 165 Hz. If the speed of waves on the string is given as 120 m/s, what is the string’s length? A. 0.36 m B. 0.73 m C. 1.1 m D. 1.4 m 𝒏.𝒗 𝟐×𝟏𝟐𝟎 𝟏𝟐𝟎 𝟏𝟐𝟎 𝒇𝒏 = ⟹ 𝟏𝟔𝟓 = = ⟹ 𝑳 = 𝟏𝟔𝟓 = 𝟎. 𝟕𝟑 𝒎 𝟐𝑳 𝟐𝑳 𝑳 Emirates National Schools- Al Ain AY 2024-2025 18  Examples calculation type questions: 11. Vibration of a certain frequency produces a standing wave on a stretched string that is 1.6 m long. The standing wave has 6 nodes and 5 antinodes. What is the wavelength of the wave that produces this standing wave? 𝟐𝑳 𝟐×𝟏.𝟔 𝝀𝒏 = = = 𝟎. 𝟔𝟒 𝒎 𝒏 𝟓 12. What is the fundamental frequency of a 0.20 m long organ pipe that is closed at one end, when the speed of sound in the pipe is 352 m/s? 𝒏.𝒗 𝟏×𝟑𝟓𝟐 𝒇𝒏 = ⟹ 𝒇𝟏 = 𝟒×𝟎.𝟐𝟎 = 𝟒𝟒𝟎 𝑯𝒛 𝟒𝑳 13. Calculate the frequency of the third harmonic on a vibrating violin string of length 50 cm. The speed of the wave on the string is 105 m/s. 𝒏.𝒗 𝟑×𝟏𝟎𝟓 𝒇𝒏 = ⟹ 𝒇𝟑 = 𝟐×𝟎.𝟓𝟎 = 𝟑𝟏𝟓 𝑯𝒛 𝟐𝑳 14. A violin string has a length of 0.54 𝑚. At the 5th harmonic the speed of the wave travelling along this string is 565 m/s. Calculate the following: a) The wavelength of the 5th harmonic. b) The frequency of the 5th harmonic. 𝟐𝑳 𝒏. 𝒗 𝝀𝒏 = 𝒇𝒏 = 𝒏 𝟐𝑳 𝟐×𝟎.𝟓𝟒 𝟓 × 𝟓𝟔𝟓 𝝀𝟓 = = 𝟎. 𝟐𝟐 𝒎 𝒇𝟓 = = 𝟐𝟔𝟏𝟔 𝑯𝒛 𝟓 𝟐 × 𝟎. 𝟓𝟒 15. What is the fundamental frequency of a guitar string of length 75 cm when the speed of waves on the string is 115 m/s? 𝒏.𝒗 𝟏×𝟏𝟏𝟓 𝒇𝒏 = ⟹ 𝒇𝟏 = 𝟐×𝟎.𝟕𝟓 = 𝟕𝟕 𝑯𝒛 𝟐𝑳 Emirates National Schools- Al Ain AY 2024-2025 19  LIGHT Review notes Electromagnetic waves: Light is made up from 7 elementary colours, namely red, orange, yellow, green, blue, indigo and violet (rainbow colours). Not all light is visible to the human eye, however. Various forms of radiation, like X-rays and radio waves, have the same characteristics as light. The reason: these are all examples of electromagnetic waves. Electromagnetic waves: An electromagnetic wave is a wave that consists of oscillating electrical and magnetic fields, which radiate outward from the source at the speed of light. In electromagnetic waves, the electrical and magnetic fields oscillate perpendicular to the direction that the wave moves and are perpendicular to each other as well. Therefore, electromagnetic waves are transverse waves. Unlike mechanical waves, electromagnetic waves can travel through a vacuum, but it can also travel through a medium (gas, liquid, solid) Speed of electromagnetic waves: All electromagnetic waves travel at the same speed in a vacuum, namely at the speed of light. For calculations, the speed of light (shown with the symbol c) is equal 𝟑. 𝟎 × 𝟏𝟎𝟖 𝒎/𝒔 For electromagnetic waves, the wave speed formula is shown alongside. Electromagnetic spectrum: Electromagnetic waves are distinguished by their different frequencies and wavelengths. In visible light, these differences in frequency and wavelength is the reason for differences in color. In the spectrum, radio waves have the lowest frequency, longest wavelengths, and have the least amount of energy. Gamma rays have the highest frequency, shortest wavelengths, and the highest amount of energy. Emirates National Schools- Al Ain AY 2024-2025 20  Examples multiple choice questions: _____ 1. Electromagnetic waves consist of ___________ electric and magnetic fields. a. oscillating b. constant c. parallel d. longitudinal _____ 2. Which of the following statements correctly describes electromagnetic waves? a. The electric and magnetic fields are at right angles to each other. b. The electric and magnetic fields are at right angles to the direction that the wave is moving. c. Electromagnetic waves are transverse waves. d. All of the above. _____ 3. All electromagnetic waves have the same ______________ a. wavelengths b. frequency c. speed d. period. _____ 4. Which one of the types of electromagnetic waves given below has the longest wavelengths? a. Gamma rays. b. Radio waves. c. Visible light. d. X-rays. _____ 5. As you move from gamma rays to microwaves, the wavelengths ___________ in length, which means that the energy of the waves are ____________. a. increase ; decreasing. b. increase ; increasing. c. decrease ; increasing. d. decrease ; decreasing. Examples calculation type questions: 6. Calculate the wavelength of the FM radio band at 94.7 MHz. (2pts) 𝟑.𝟎×𝟏𝟎𝟖 𝝀 = 𝟗𝟒.𝟕×𝟏𝟎𝟔 = 𝟑. 𝟐 𝒎 7. Determine the frequency of highly energetic ultraviolet radiation that has a wavelength of 125 nm. (2pts) 𝟑.𝟎×𝟏𝟎𝟖 𝒇 = 𝟏𝟐𝟓×𝟏𝟎−𝟗 = 𝟐. 𝟒 × 𝟏𝟎𝟏𝟓 𝑯𝒛 Emirates National Schools- Al Ain AY 2024-2025 21  Reflection off a plane mirror: Reflection of llight: Reflection is the change in direction of an electromagnetic wave at a surface that causes it to move away from the surface. Laws of reflection: The laws of reflection are: 1. The angle of incidence and the angle of reflection are always equal (𝜃𝑖 = 𝜃𝑟 ). 2. The incident ray, the reflected ray and the normal at the point of reflection all lie in the same plane. The normal is a line drawn perpendicular to the surface of the material at the point where the light ray strikes the surface. The angle of incidence (𝜃𝑖 ) is the angle between the incoming ray (incident ray) and the normal. The angle of reflection (𝜃𝑟 ) is the angle between the normal and the ray that is reflected. Surface of reflection: The surface of the material that the light rays strike affects the way reflection takes place. a) All incident light rays are parallel to one another. If these rays hit a rough, uneven surface (like paper, rough wood or the ground), the reflected rays will scatter in all directions and the rays are not parallel any more. This type of reflection is called diffuse reflection. b) If the parallel incident rays hit a smooth surface (like a mirror, polished wood or a calm water surface), the reflected rays are reflected in parallel, all in the same direction. This type of reflection is called specular reflection. Plane mirror (also called flat mirror): A plane mirror is an example of a smooth surface where specular reflection causes all the light rays to reflect in parallel, therefore creating a virtual image of an object inside the mirror, at the same distance from the mirror’s surface as the object is located. The image formed by rays that appear to come from the image point behind the mirror – that does not really exist – is called a virtual image. Images formed by a plane mirror is upright, but left-right inverted. Properties of plane mirror images: The plane mirror image position: 𝒙𝒐 = −𝒙𝒊 𝒐𝒃𝒋𝒆𝒄𝒕 𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆 = −𝒊𝒎𝒂𝒈𝒆 𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆 (the – sign shows a virtual image) ℎ𝑜 ℎ𝑖 The plane mirror image height: 𝒉𝒐 = 𝒉𝒊 𝒐𝒃𝒋𝒆𝒄𝒕 𝒉𝒆𝒊𝒉𝒕 = 𝒊𝒎𝒂𝒈𝒆 𝒉𝒆𝒊𝒈𝒉𝒕 𝑥𝑜 𝑥𝑖 Emirates National Schools- Al Ain AY 2024-2025 22  Examples multiple choice questions: 1. The type of reflection showed in the diagram in Reflection A can be described as …. A. diffuse reflection from smooth surfaces. B. diffuse reflection from uneven surfaces. C. specular reflection from smooth surfaces. D. specular reflection from uneven surfaces. 2. If a light ray strikes a plane mirror at an incident angle of 20°, the ray will reflect at an angle of … A. 20° from the mirror surface. B. 20° from the normal. C. 10° from the normal. D. 40° from the mirror surface. 3. In the diagram alongside, which letter represents the normal? A. Letter A B. Letter B C. Letter C D. Letter E 4. In the diagram alongside, which letter shows the angle of reflection? A. Letter A B. Letter B C. Letter C D. Letter D 5. When an object is reflected in a plane mirror, the image you see is … A. virtual and upright. B. virtual and inverted. C. real and upright. D. real and inverted. 6. A capital letter R is placed in front of a plane mirror. Which answer below shows the correct image of the object? Examples calculation type questions: 7. In each of the following examples, write down if the type of reflection is specular or diffuse reflection: a. Reflection of light from the surface of a lake on a calm day Specular b. Reflection of light from a plastic trash bag Diffuse c. Reflection of light from the lens of eyeglasses Specular d. Reflection of light from a carpet Diffuse Emirates National Schools- Al Ain AY 2024-2025 23 8. Two flat mirrors make an angle of 90° with each other, as shown. An incoming ray makes an angle of 25° with the normal of mirror A. Use the law of reflection to determine the angle of reflection from mirror B. Answer = 65° 90 – 25 = 65° 𝜃𝑖 65° 90° 25° 25° 9. A boy is looking towards plane mirror on a wall which is 2.0 m away from him, as shown. He sees a picture that is located 0.2 m behind him in the mirror. State the following: a. The distance between the picture and the mirror is _2.2 m_(0.2 + 2.0)_______________ b. The distance between the boy and his image is _4.0 m_(2.0 + 2.0)_______________ c. The distance between the boy and the image of the picture is 0.2 2.0 _4.2 m_(2.0 + 2.2)_______________ d. The distance between the picture and the image of the picture is _4.4 m_(2.2 + 2.2)_______________ GOOD LUCK WITH YOUR STUDIES!! Emirates National Schools- Al Ain AY 2024-2025 24