Doppler Effect: Grade 12 Past Paper Questions

A bat emits sound waves with a frequency fs as it flies at a constant speed vB towards a vertical cliff. The waves reflect off the cliff with the same frequency that they strike the cliff, and with a wavelength of λL = 0,016 m, as shown in the simplified diagram below. Take the speed of sound in air to be 340 m·s⁻¹. 6.1 NAME and STATE the phenomenon that results in a change in frequency of the detected sound waves. 6.2 Show that fs, the frequency of the sound waves emitted by the bat, is (21 250 – 62,5vB). 6.3 The frequency of the reflected sound waves detected by the bat is 850 Hz higher than the frequency of the sound waves emitted by the bat. Calculate the speed of the bat, vB.

A stationary listener, standing on the roadside, records the wavelength of the sound emitted by the siren of a police car travelling at a constant velocity. In the wavelength-time graph below, NOT drawn to scale, λL is the wavelength of the sound recorded by the listener and λS is the wavelength of the sound emitted by the siren. Take the speed of sound in air to be 343 m·s⁻¹. 6.1 Name the phenomenon that explains why the wavelengths shown in the graph differ. 6.2 Is the car moving TOWARDS or AWAY FROM the listener? Give a reason for the answer. 6.3 Calculate the: 6.3.1 Frequency of the sound emitted by the siren. 6.3.2 Magnitude of the velocity of the car.

A stationary listener records the frequency of the sound emitted by the siren of a police car. When the car, which is travelling at a constant velocity of 26 m·s⁻¹, approaches the listener, the recorded frequency is 615 Hz. The car passes the listener at time t1 and then moves away from the listener. The recorded frequency now is 526 Hz. Ignore the effects of wind. 6.1 State the Doppler effect in words. 6.2 Use the information given to calculate the speed of sound in air. 6.3 Calculate the wavelength of the sound emitted by the police siren. 6.4 Sketch the graph of recorded frequency versus time for the motion of the car as it moved towards the listener, passed the listener and then moved away from the listener. Label time t1 on the graph. No values need to be indicated on the frequency axis.

6.1 A car moves at a constant velocity of 22 m·s⁻¹ on a straight horizontal road TOWARDS a stationary device, which can both emit and detect sound waves. The device emits sound waves with a frequency of 24 000 Hz. These sound waves are reflected off the car and the reflected sound waves are then detected by the device, as shown in the diagram below. 6.1.1 State the Doppler effect in words. 6.1.2 If the speed of sound in air is 340 m·s⁻¹, calculate the frequency of the reflected sound waves detected by the device. 6.2 The spectral lines observed for a distant star show that the star is moving away from Earth. Explain, by referring to frequency, how one can deduce that the star is moving away from Earth.

A learner investigates the relationship between the observed frequency and the frequency of sound waves emitted by a stationary source. The learner moves towards the source at a constant velocity and records the observed frequency (fL) for a given source frequency (fS). This process is repeated for different frequencies of the source, with the learner moving at the same constant velocity each time. The graph below shows how the observed frequency changes as the frequency of sound waves emitted by the source changes. 6.1 Name the phenomenon illustrated by the graph. 6.2 Name ONE application in the medical field of the phenomenon in QUESTION 6.1. 6.3 Write down the type of proportionality that exists between fL and fS, as illustrated by the graph. 6.4 The gradient of the graph obtained is found to be 1,06. If the speed of sound in air is 340 m·s⁻¹, calculate the magnitude of the velocity at which the learner approaches the source. The investigation is now repeated with the learner moving at a HIGHER constant velocity towards the sound source. 6.5 Copy the graph above in your ANSWER BOOK and label it as A. On the same set of axes, sketch the graph that will be obtained when the learner is moving at the HIGHER velocity. Label this graph as B.

The siren of a stationary ambulance emits sound waves at a constant frequency of 680 Hz. A man is standing with a detector that records the wavelength of the sound emitted by the siren, as shown in the diagram below. The speed of sound in air is 340 m·s⁻¹. 6.1 Calculate the wavelength of the detected sound. The ambulance now moves at a constant speed along the road TOWARDS the man. The detector now records the wavelength of the sound, which differs from the previous reading by 0,05 m. 6.2 State the Doppler effect. 6.3 How would EACH of the following have changed when the ambulance approached the detector compared to when the ambulance was stationary? Choose from INCREASED, DECREASED or NO CHANGE. 6.3.1 Distance between the wave fronts. 6.3.2 Frequency of the detected waves. 6.4 Calculate the speed of the ambulance.

A group of grade 12 learners investigates the relationship between the RATIO of the observed frequency to the frequency of the source (fL/fS), and the velocity at which the listener moves relative to a stationary source. The experiment is repeated by increasing the constant velocity at which the listener moves towards the same sound source. The observed frequency (fL) is recorded and the RATIO (fL/fS) for each experiment is calculated. The graph below shows the results that were acquired. 7.1 State the Doppler effect in words. Use the graph to answer the following questions. 7.2 Is the listener moving AWAY or TOWARDS the stationary source? Give a reason for the answer. 7.3 What physical quantity is represented by the gradient of this graph? 7.4 Calculate the speed of sound in air.

6.1 A stationary sound source (S) produces sound with a frequency of 170 Hz. A listener (L) in a car travelling at a constant speed of 12 m·s⁻¹ towards this source, observes the frequency of the sound as x Hz. Take the speed of sound in air to be 340 m·s⁻¹. 6.1.1 State the Doppler effect in words. 6.1.2 Will the observed frequency INCREASE, DECREASE or REMAIN THE SAME if: (a) the constant speed of the car moving towards the stationary sound source is greater than 12 m·s⁻¹; (b) the sound produced by the source is louder. The frequency of the sound source is changed. The listener now travels towards the stationary sound source at a constant speed of 24 m·s⁻¹. The observed frequency is still x Hz. 6.1.3 Calculate the new frequency of the sound source. 6.2 X, Y and Z are absorption spectra. B and R represent the blue and red ends of the spectra. Spectrum X shows the absorption lines of light from the sun. Which spectrum shows the absorption lines of light from another star that is moving AWAY from Earth? Choose from X, Y or Z. Explain the answer.

A bat flies away from a stationary bat watcher at a constant velocity. The bat constantly emits sound waves at a frequency of 875 Hz. The bat watcher hears a change in pitch as the bat moves away from her. 6.1 Write down the property of sound that is related to pitch. 6.2 Give a reason why the bat watcher observes a change in pitch as the bat moves away from her. Shown below is the air pressure versus distance graph, which represents the sound waves detected by the bat watcher as the bat moves away from her with a constant velocity. The speed of sound in air is 340 m·s⁻¹. 6.3 Use the graph to write down the wavelength of the detected waves. 6.4 Determine the: 6.4.1 Frequency of the sound waves detected by the bat watcher. 6.4.2 Velocity at which the bat flies.

1.6 The spectrum of helium emitted from a star moving away from Earth is compared to the spectrum of helium found on Earth. Which ONE of the following statements is CORRECT? The observed spectral lines from the moving star will have a … A. lower frequency and a longer wavelength. B. lower frequency and a shorter wavelength. C. higher frequency and a shorter wavelength. D. higher frequency and a longer wavelength. 1.7 The magnitudes of electric fields generated by different point charges are measured at a fixed point. For each measurement, the distance between this fixed point and the charges are the same. Which ONE of the following sketch graphs CORRECTLY shows the relationship between the magnitude of the electric field (E) and the magnitude of the charge (Q)?

1.5 A ball falling vertically downwards from point A strikes the ground with velocity v and bounces, reaching a maximum height at point B, as shown in the diagram below. Which ONE of the combinations below is CORRECT for the direction of the impulse on the ball upon striking the ground and the magnitude of the velocity with which the ball leaves the ground? A. Upward, greater than v. B. Downward, greater than v. C. Upward, less than v. D. Downward, less than v. 1.6 The absorption spectrum of an element surrounding a moving star is observed on Earth and found to be red shifted. Which ONE of the following combinations is CORRECT for the movement of the star and the frequency of the observed light on Earth? A. Away from Earth, decreased. B. Towards Earth, decreased. C. Away from Earth, increased. D. Towards Earth, increased.

1.5 A hot-air balloon is moving vertically downwards at a CONSTANT SPEED. Assume that the mass of the hot-air balloon remains constant. Which ONE of the following physical quantities associated with the hot-air balloon changes during the motion? A. Weight. B. Momentum. C. Kinetic energy. D. Potential energy. 1.6 A learner standing at a roadside records the frequency of sound waves produced by the siren of an ambulance. The ambulance is moving at constant velocity along a straight horizontal road. The frequency-time graph for the detected sound is shown below. Which ONE of the following statements concerning the motion of the ambulance is CORRECT? The ambulance … A. approaches the learner and then passes the learner. B. moves away from the learner, then turns and approaches the learner. C. approaches the learner, then turns and moves away from the learner. D. moves away from the learner and then stops.

QUESTION 6: A traffic officer is sitting in a police car which is travelling at a constant velocity. The siren of the police car emits sound waves of frequency 1500 Hz. A detector that is placed on the side of the road records a frequency of 1695 Hz. The police car takes 1,5 s to reach the detector. Take the speed of sound in air as 340 m·s⁻¹. 6.1 Name and state the phenomenon described above. 6.2 Write down ONE medical instrument that makes use of the phenomenon in QUESTION 6.1. 6.3 Calculate the distance between the police car and the detector. 6.4 Draw a graph of the frequency heard by the traffic officer sitting in the police car as it moves towards and away from the detector, versus time. Indicate the following on the graph: the frequency heard by the traffic officer; the time taken by the police car to reach the detector. QUESTION 7: Three point charges, X, Y and Z, with charges of -3 µC, +6 µC and +9 µC respectively, are placed on insulated stands as shown below. 7.1 State Coulomb's law in words. 7.2 Calculate the net force acting on point charge Z. 7.3 Point charges X and Y are brought into contact and then separated. Point charge X is returned to its original position, while point charge Y is removed. 7.3.1 In which direction did electrons flow? Choose from X to Y or Y to X. 7.3.2 Calculate the number of electrons transferred to or from point charge X. 7.3.3 Point T is placed between point charges X and Z. Calculate the distance between point charges X and T where the net electric field is equal to zero.

1.4 A ball is thrown vertically upwards into the air. Ignore the effects of air friction. The net force acting on the ball when the ball is at its highest point is ... A. Zero. B. Equal to the weight of the ball. C. Less than the weight of the ball. D. Greater than the weight of the ball. 1.5 Which ONE of the following statements is always true for inelastic collisions in an isolated system? A. Both momentum and kinetic energy are conserved. B. Both momentum and kinetic energy are not conserved. C. Momentum is conserved, but kinetic energy is not conserved. D. Kinetic energy is conserved, but momentum is not conserved. 1.6 An object moving horizontally at a constant velocity suddenly encounters a rough horizontal surface. The object continues to move over this rough surface. Which ONE of the following statements is correct? The net work done on the object during the motion over the rough surface is ... A. Zero. B. Positive. C. Negative. D. Constant. 1.7 The hooter of a car emits sound of constant frequency as the car moves away from a stationary listener. Which ONE of the following properties of the sound heard by the listener will NOT change? A. Speed. B. Frequency.

1.5 Consider the two spectrum diagrams below. Diagram 1 represents the spectrum of an element in a laboratory on Earth. Diagram 2 represents the spectrum of the same element from a distant star as observed from Earth. Which ONE of the following can be deduced from the spectra above? A. The star is moving towards Earth. B. The star is at rest relative to Earth. C. The star is moving away from Earth. D. Both the star and Earth are moving towards each other. 1.6 The diagram below shows the field lines for the combined electric field due to two small charged spheres P and Q. Which ONE of the combinations below correctly shows the polarity of spheres P and Q? A. Sphere P: negative; sphere Q: positive. B. Sphere P: negative; sphere Q: negative. C. Sphere P: positive; sphere Q: positive. D. Sphere P: positive; sphere Q: negative.

1.6 The ratio of the wavelength of sound produced by a stationary source (λₛ) to the wavelength of the sound detected by a listener (λₗ) is 1:1,09. The listener is moving at constant velocity. The frequency of the source is fₛ and the frequency detected by the listener is fₗ. Which ONE of the following combinations of fₗ and the movement of the listener is CORRECT? A. Greater than fₛ; towards the source. B. Greater than fₛ; away from the source. C. Less than fₛ; towards the source. D. Less than fₛ; away from the source. 1.7 R and S are two NEGATIVE point charges of equal magnitude. P is a point to the left of R. Point P and charges R and S are on the same horizontal line. Which ONE of the following vector diagrams, drawn to scale, of the electric fields Eᵣ due to R, and Eₛ due to S, at point P, is CORRECT?

1.4 A person of mass M is moving to the left on a skateboard of mass m. The initial velocity of the person and the skateboard is v. The person then jumps off the skateboard and is stationary while the skateboard continues to move to the left. Which of the following expressions can be used to correctly calculate the speed of the skateboard after the person jumps off? A. (M+m)v/m. B. (Mv+mv)/m. C. mv/(M+m). D. (M−m)v/m. 1.5 An apple falls from a tree. Which of the following statements about the falling apple is TRUE? Ignore all effects of air friction. A. Total momentum is conserved. B. Total kinetic energy is conserved. C. The total mechanical energy is conserved. D. The gravitational potential energy is conserved. 1.6 An ambulance moves towards a stationary listener at a constant speed while emitting soundwaves with a wavelength of 0,72 m. The wavelength of a soundwave observed by the listener becomes ... A. Larger than 0,72 m. B. Smaller than 0,72 m. C. Equal to 0,72 m. D. Larger and then zero.

1.4 A trolley with a mass m has momentum p. The kinetic energy of the trolley will be: A. pm. B. p/m. C. pm/2. D. p²/(2m). 1.5 An object is moved from rest in a straight line across a flat surface by a changing horizontal force. The changing force is plotted against the position of the object to produce the graph below. The work done on the object by the applied force from x = 0 m to x = 8 m is: A. 40 J. B. 80 J. C. 108 J. D. 125 J. 1.6 The reason why the observed pitch of the sound wave of an ambulance decreases as the ambulance moves away from a stationary observer is because the: A. amplitude of the sound wave increases. B. amplitude of the sound wave decreases. C. wavelength of the sound wave increases. D. wavelength of the sound wave decreases.