Doppler effect for sound waves

For which kinds of wave can the Doppler shift be observed?

Feb/March 2016

A star far away is moving away from Earth at a speed of $1.40 \times 10^{7}\,\text{m s}^{-1}$. It gives out light with a frequency of $4.57 \times 10^{14}\,\text{Hz}$. The speed of light is $3.00 \times 10^{8}\,\text{m s}^{-1}$. The Doppler effect formula may be applied to light waves. What frequency will this light have when it is observed on Earth?

Feb/March 2016

A source of sound waves is moving as illustrated. In which case would the stationary observer notice the greatest drop in the observed frequency?

Feb/March 2017

State the meaning of the Doppler effect.

Feb/March 2017

A vehicle is fitted with a microwave transmitter that produces microwaves at a fixed frequency. A stationary observer has a microwave receiver. The vehicle travels straight towards the observer at constant speed. The observer detects microwaves with frequency $F_o$. The vehicle then speeds up, while still moving towards the observer, continues at a larger constant speed for a period and then slows down until it comes to rest. How does the frequency of the microwaves detected by the observer change?

Feb/March 2018

A buzzer that produces sound with frequency $846\ \text{Hz}$ is fixed to a string and whirled in a horizontal circle. Its linear speed is $25.0\ \text{m s}^{-1}$. The speed of sound is $340\ \text{m s}^{-1}$. What is the maximum frequency heard by the observer?

Feb/March 2019

An observer is positioned at the summit of a tall tower. An aeroplane that is emitting sound with a frequency of $1000\,\text{Hz}$ moves towards the observer at a speed of $165\,\text{m s}^{-1}$. The speed of sound is $330\,\text{m s}^{-1}$. What frequency does the observer receive for the sound?

Feb/March 2020

The dolphin is moving underwater at a steady speed of $4.50\,\text{m s}^{-1}$.

Feb/March 2020

A source producing sound with frequency $F$ at point $Z$ is travelling at a constant speed. The arrangement of the emitted wavefronts is shown. Which row gives the sound frequencies detected by stationary observers at $X$ and $Y$?

Feb/March 2021

A sound source is tied to a rope and whirled round in a horizontal circle at constant speed, as shown in Fig. 5.1. The source has speed $12.0\,\text{m s}^{-1}$ and emits sound with frequency $951\,\text{Hz}$. The speed of sound in air is $330\,\text{m s}^{-1}$. An observer, positioned very far from the source, hears the sound.

Feb/March 2021

An ambulance emits a warning signal at a frequency of $600\,\text{Hz}$. The speed of sound is $330\,\text{m s}^{-1}$. The ambulance moves at a constant velocity of $25\,\text{m s}^{-1}$ towards an observer. After it passes, it continues travelling away from the observer with the same velocity. What net change in the observed frequency occurs from the time when the ambulance is far behind the observer to the time when it is far in front of the observer?

Feb/March 2022

State the conditions needed for a stationary wave to be formed.

Feb/March 2022

A source of sound waves that has a constant frequency is moving towards an observer who is stationary. The observer compares the sound waves reaching the observer’s position with the waves produced by the source of sound. What is detected by the observer?

Feb/March 2024

The diagram illustrates a car moving from point X to point Y in a straight path at a steady speed between person P and person Q. As it moves, the car keeps its horn sounding all the time. The horn produces sound with a fixed frequency. Which of the following statements about the sounds heard by person P and person Q during the car’s movement are correct? 1. Person P hears a sound whose frequency increases. 2. Person Q hears a sound whose frequency decreases. 3. Person Q always hears a sound with a higher frequency than person P.

Feb/March 2025

A loudspeaker at rest produces sound with a constant frequency. A microphone is positioned close to the loudspeaker and linked to a cathode-ray oscilloscope (CRO). The trace displayed on the CRO screen is shown in Fig. 5.1. The CRO time-base is adjusted to $5.0 \times 10^{-4}\,\text{s cm}^{-1}$.

Feb/March 2025

A source producing sound with frequency $1000\,\text{Hz}$ travels away from an observer who is at rest at a speed of $30.0\,\text{m s}^{-1}$. The speed of sound is $330\,\text{m s}^{-1}$. What frequency of sound does the observer hear?

May/June 2016

As a car moving at constant velocity passes an observer at rest, the observer notices a change in the frequency of the sound produced by the car. Which statement is correct?

May/June 2016

Using the direction of energy propagation as your reference, state what is meant by a longitudinal wave and by a transverse wave.

May/June 2016

A car moving along a straight path at a speed of $30\,\text{m s}^{-1}$ passes a stationary observer while its horn is sounding. The actual frequency of the sound from the horn is $400\,\text{Hz}$. The speed of sound in air is $336\,\text{m s}^{-1}$. What is the change in the frequency of the sound heard by the observer as the car goes past?

May/June 2017

An ambulance is moving along a straight road at a speed of $30.0\,\text{m s}^{-1}$. The siren on the ambulance produces sound with a frequency of $2000\,\text{Hz}$. The speed of sound in air is $340\,\text{m s}^{-1}$. As the ambulance goes past a man who is standing at the roadside, what frequency does he hear while the ambulance is approaching him, and what frequency does he hear while it is moving away from him?

May/June 2017

A stationary observer is approached by a high-speed train travelling at a speed of $80\,\text{m s}^{-1}$. The horn on the train produces a sound with frequency $250\,\text{Hz}$. The speed of sound is $340\,\text{m s}^{-1}$. What frequency is observed from the horn?

May/June 2017

Describe what is meant by the Doppler effect.

May/June 2017

Define the frequency of a sound wave.

May/June 2017

A binary star is made up of two stars that orbit a shared centre. Light from one star is detected on the Earth. The measured frequency of the light changes from a minimum frequency $f_{\min}$ to a maximum frequency $f_{\max}$, as shown. The rotation rate of the binary star rises. How do $f_{\max}$ and $f_{\min}$ change?

May/June 2018

An astronomer studies the light coming from a star that is receding from the Earth. For the light that is observed, which quantity has increased because of the star’s motion?

May/June 2018

A police car moves with a velocity of $30.0\,\text{m s}^{-1}$ directly towards an observer who is at rest. The car horn produces sound at a frequency of $2000\,\text{Hz}$. The speed of sound is $340\,\text{m s}^{-1}$. What is the frequency of the sound received by the observer?

May/June 2018

An insect at rest on the water surface produces circular ripples using its legs, as shown in diagram 1. The insect then starts moving to the right, as shown in diagram 2. Which row describes how the movement of the insect changes the waves at $X$?

May/June 2019

A toy motorboat is travelling with constant velocity $v$ and bobs vertically on the surface of a pond. As a result, the boat produces circular water waves with frequency $2.0\,\text{Hz}$. The wave speed is $1.5\,\text{m s}^{-1}$. A man who is standing by the pond’s edge notices that the waves arriving from the boat have a frequency of $3.0\,\text{Hz}$. The equation used for Doppler effect calculations for sound waves can also be applied to water waves. What is a possible value of $v$?

May/June 2019

In one of the earliest experiments used to show the Doppler effect, a train was packed with trumpeters, each of whom played a note of frequency $440\,\text{Hz}$. When the train moved directly towards a stationary observer, the change in the observed frequency of the note was $22\,\text{Hz}$. The speed of sound was $340\,\text{m s}^{-1}$. At which speed was the train moving?

May/June 2019

A motor boat oscillates in the water and generates water waves with frequency $0.20\,\text{Hz}$. These waves travel through the water at $20\,\text{m s}^{-1}$. The motor boat is moving at $5.0\,\text{m s}^{-1}$ straight towards a sailing boat that is stationary. The Doppler effect equation for sound waves is also valid for water waves. What frequency do the waves arrive at the stationary sailing boat with?

May/June 2019

A sound source producing a tone of one frequency $f_s$ moves at a steady speed straight toward an observer. It then goes past the observer and keeps moving straight away from the observer. The source velocity is unchanged. Which graph shows how the frequency $f_o$ of the sound detected by the observer varies with time?

May/June 2020

A person who is not moving measures the speed and wavelength of the sound produced by a horn on a vehicle that is also not moving. The person then carries out the measurements again while the vehicle is moving towards them at a constant speed. Which row states the measured wavelength and the measured speed of the sound wave from the moving vehicle in comparison with the sound wave from the vehicle at rest?

May/June 2020

A sound wave with frequency $f$ is produced by a source S that is not moving. The source then travels away from an observer who remains stationary. Which statement is correct?

May/June 2020

An ambulance has a siren that produces sound at a fixed frequency. The ambulance is travelling straight towards a stationary observer. As the ambulance gets closer to the observer, it slows down, and after it has gone past the observer, it speeds up. How does the frequency of the sound heard by the observer change while the ambulance is approaching and while it is moving away from the observer?

May/June 2021

A person is standing beside a straight railway line. A train travels towards the person and sound is produced by its whistle. As the train comes nearer, the person hears a sound with frequency $1690\,\text{Hz}$. When the train has passed and is moving away, the person hears a sound with frequency $1500\,\text{Hz}$. The speed of sound in air is $340\,\text{m s}^{-1}$. Determine the speed of the train.

May/June 2021

A train whistle produces sound with frequency $500\,\text{Hz}$ while the train travels at a speed of $20\,\text{m s}^{-1}$ along a straight track. The train is moving straight towards a stationary observer beside the track, and then it goes past the observer. The speed of sound in air is $330\,\text{m s}^{-1}$. What is the difference between the frequencies of the sound heard by the observer before the train passes and after it has passed the observer?

May/June 2021

A car is moving with a constant velocity straight towards a man who is standing in the centre of the road. The driver uses the car’s horn to give a warning. The horn produces a sound wave with a constant frequency. The frequency of the sound received by the man is not the same as the frequency of the sound produced by the horn. Which statement is correct?

May/June 2022

A source produces a sound wave with one frequency. Owing to the Doppler effect, a stationary observer hears sound at a different frequency. What condition is necessary for the Doppler effect to happen?

May/June 2022

A man beside a train at rest detects a sound with frequency $400\ \text{Hz}$ produced by the train’s horn. The train then travels directly away from the man and sounds its horn while moving at $50\ \text{m s}^{-1}$. The speed of sound in air is $340\ \text{m s}^{-1}$. What is the difference between the frequencies of the sound heard by the man in the two situations?

May/June 2022

The car moves at constant speed in a straight line PQ. A loudspeaker fixed to the car emits sound with constant frequency $f$. A stationary observer is located at point O. What sound does the observer hear while the car travels from P to Q?

May/June 2023

A source X produces a sound wave with a steady frequency $f$. This wave is then detected by a stationary detector Y. The frequency measured by Y is smaller than $f$. What could explain this?

May/June 2023

A vehicle travels at constant velocity along a road straight towards an observer. As it goes past the observer, the frequency detected from the vehicle’s sound alters. Which phenomenon accounts for this change in frequency?

May/June 2023

A siren on a police car that is moving produces sound waves of frequency $440\,\text{Hz}$. A fixed observer detects a sound frequency of $494\,\text{Hz}$. The speed of sound in air is $340\,\text{m s}^{-1}$. What are the possible speed and direction of travel of the car?

May/June 2024

A man is standing still in front of a swing. A child is seated on it and swinging. The child sounds a whistle that produces a note at a steady frequency. The man notes the frequency of the sound when the swing is at positions X, Y and Z. At which position will the man hear the greatest frequency?

May/June 2024

An ambulance siren produces a sound of single frequency $f$. The ambulance moves towards a stationary observer, passes very close by, and then moves away from the observer. Which statement gives the frequency of the sound detected by the observer as the ambulance goes past?

May/June 2024

An aircraft emits a sound with frequency of $30.0\,\text{Hz}$. The speed of sound in air equals $330\,\text{m s}^{-1}$. The aircraft is positioned directly in front of a stationary observer and moves in a straight line either towards the observer or away from the observer. The observer detects the aircraft’s sound at a frequency of $20.0\,\text{Hz}$. What is the aircraft’s speed and direction?

May/June 2025

A buzzer that produces sound at a frequency of $846\,\text{Hz}$ is fixed to a string and spun in a horizontal circle. Its linear speed is $25.0\,\text{m s}^{-1}$. Take the speed of sound as $340\,\text{m s}^{-1}$. What is the largest frequency detected by the observer?

May/June 2025

A vehicle is travelling at a speed of $30.0\,\text{m s}^{-1}$ straight towards an observer who is stationary. The vehicle’s horn produces a sound with frequency $440\,\text{Hz}$. The speed of sound in air is $340\,\text{m s}^{-1}$. What is the frequency of the sound heard by the observer?

May/June 2025

Use the definitions of speed $v$, frequency $f$ and wavelength $\lambda$ to obtain the wave equation $v = f\lambda$.

May/June 2025

An ambulance’s warning signal has a frequency of $600\,\text{Hz}$. The speed of sound is $330\,\text{m s}^{-1}$. The ambulance moves at a constant velocity of $25\,\text{m s}^{-1}$ towards an observer. What overall change in the observed frequency occurs from when the ambulance is far behind the observer to when it is far in front of the observer?

Oct/Nov 2016

A man beside a train that is at rest hears a sound of frequency $400\,\text{Hz}$ coming from the train’s horn. The train then travels directly away from the man and blows its horn when it is moving at a speed of $50\,\text{m s}^{-1}$. The speed of sound is $340\,\text{m s}^{-1}$. What is the change in frequency of the sound heard by the man between the two cases?

Oct/Nov 2016

An ambulance emits a warning signal with a frequency of $600\,\text{Hz}$. The speed of sound is $330\,\text{m s}^{-1}$. The ambulance moves towards an observer at a steady velocity of $25\,\text{m s}^{-1}$. What total change in the observed frequency occurs from the moment when the ambulance is far behind the observer to the moment when it is far ahead of the observer?

Oct/Nov 2016

State what the frequency of a progressive wave means.

Oct/Nov 2016

State what is meant by the frequency of a progressive wave.

Oct/Nov 2016

The Sun emits light with a specific wavelength $\lambda_s$. However, at a given moment, the Earth records a spread of wavelengths extending from values below $\lambda_s$ to values above $\lambda_s$. This happens because of the Doppler effect. What might account for this Doppler effect?

Oct/Nov 2017

A train travelling along a railway track in a straight line has a whistle that emits sound continuously at frequency $f$. A woman standing beside the track hears a sound with frequency $0.85f$. The speed of sound in air is $340\,\text{m s}^{-1}$. What is the train’s velocity?

Oct/Nov 2017

A sound source with frequency $F$ at point $Z$ is travelling at a constant speed. The arrangement of the wavefronts it emits is shown. Which row gives the frequencies of the sound detected by stationary observers at $X$ and $Y$?

Oct/Nov 2017

A car is moving in a straight line at constant speed and passes near a stationary observer. The observer records the frequency of the sound produced by the engine. When the car is coming towards the observer, the measured frequency is $220\,\text{Hz}$. When the car is travelling away, the measured frequency is $180\,\text{Hz}$. The speed of sound in air is $340\,\text{m s}^{-1}$. What is the speed of the car?

Oct/Nov 2017

Explain what is meant by a longitudinal wave, with reference to the direction in which energy propagates.

Oct/Nov 2017

A jet aircraft moves with speed $0.8v$, where $v$ represents the speed of sound. The aircraft is moving towards an observer at rest. The sound produced by the aircraft has a frequency of $100\,\text{Hz}$. Which frequency is heard by the observer?

Oct/Nov 2018

A police car is fitted with a two-tone siren that produces sounds with frequencies of $700\,\text{Hz}$ and $1000\,\text{Hz}$. The car is moving at $40.0\,\text{m s}^{-1}$ towards a stationary observer. The speed of sound in air is $340\,\text{m s}^{-1}$. What is the difference between the two frequencies heard by the observer?

Oct/Nov 2018

A bat travels straight towards a stationary ultrasound detector at a speed of $25.0\,\text{m s}^{-1}$ while producing ultrasound pulses with frequency $40.0\,\text{kHz}$. The speed of sound in air is $330\,\text{m s}^{-1}$. What frequency is registered by the ultrasound detector?

Oct/Nov 2018

A siren on a police car that is moving produces a sound wave with frequency of $440\,\text{Hz}$. An observer who is not moving detects sound with frequency of $494\,\text{Hz}$. The speed of sound in air is $340\,\text{m s}^{-1}$. What might be the car’s speed and direction of travel?

Oct/Nov 2019

A loudspeaker producing a steady frequency of $2000\,\text{Hz}$ is moved in a horizontal circle at a speed of $15.0\,\text{m s}^{-1}$. A stationary observer, positioned level with the loudspeaker and far away from it, hears sound whose frequency changes. The greatest frequency heard is $2097\,\text{Hz}$. Determine the speed of sound in air.

Oct/Nov 2019

A siren produces sound with frequency $1000\,\text{Hz}$. The siren is travelling at $20\,\text{m s}^{-1}$ towards an observer who is stationary. The speed of sound in air is $330\,\text{m s}^{-1}$. Which expression gives the frequency heard by the observer correctly?

Oct/Nov 2019

A source producing sound at a frequency of $1000\ \text{Hz}$ moves directly towards a stationary observer. The observer records the frequency of the sound received as $1500\ \text{Hz}$. The speed of sound in still air is $330\ \text{m s}^{-1}$. What is the speed of the source of sound?

Oct/Nov 2020

An emergency vehicle is emitting its siren while it speeds up on a straight road between points $X$ and $Y$, as shown in the diagram. The siren produces a sound frequency of $750\,\text{Hz}$. One person is positioned at $X$ and another person is positioned at $Y$. What describes the sounds heard by the people at $X$ and at $Y$ as the vehicle accelerates?

Oct/Nov 2020

A train horn produces sound at frequency $f_1$. As the horn continues to sound, the train travels straight towards a person at rest. The train's speed is $0.20v$, where $v$ denotes the speed of sound. The frequency of the sound received by the person is $f_2$. What is the ratio $\frac{f_1}{f_2}$?

Oct/Nov 2020

For which waves can the Doppler effect be observed?

Oct/Nov 2021

A train moves along a straight track with constant speed of $30\,\text{m s}^{-1}$. Its horn emits a continuous sound at frequency $2400\,\text{Hz}$. An observer is at rest beside the railway line. As the train comes towards the observer, passes him, and then recedes. The speed of sound is $340\,\text{m s}^{-1}$. What is the greatest difference between the frequencies of the sound heard by the observer?

Oct/Nov 2021

A train moves with a constant speed on a straight track. Its horn produces a sound with frequency $500\,\text{Hz}$. A person beside the track detects a sound with frequency $450\,\text{Hz}$. The speed of sound in air is $340\,\text{m s}^{-1}$. Determine the speed of the train and state whether it is moving towards or away from the person.

Oct/Nov 2021

By referring to the direction in which energy is transferred, state what is meant by a longitudinal wave.

Oct/Nov 2021

A child is seated on the ground beside a remote-controlled car. When $t = 0$, the car starts to travel in a straight line directly away from the child. Figure 4.1 shows how the car’s velocity along this line varies with time $t$. Between $t = 0$ and $t = 6.0\,\text{s}$, the car’s horn continuously produces sound of frequency $925\,\text{Hz}$. The speed of sound in air is $338\,\text{m s}^{-1}$.

Oct/Nov 2021

A jet aircraft moves at a speed of $0.80v$, where $v$ represents the speed of sound. The aircraft is heading straight towards a stationary observer. The sound produced by the aircraft has a frequency of $100\,\text{Hz}$. What frequency is heard by the observer?

Oct/Nov 2022

A miniature loudspeaker, starting from rest, drops vertically from a window in a tall building. After it has fallen a distance of $10.0\,\text{m}$, it emits a very brief sound pulse with constant frequency $256\,\text{Hz}$ in all directions. The sound pulse, moving at a speed of $330\,\text{m s}^{-1}$, is detected by a person leaning out of the window. Air resistance is negligible. What frequency is heard by the person for the sound pulse?

Oct/Nov 2022

An observer is standing on a railway platform. A train moves past the observer at a steady speed while its whistle emits sound with constant frequency $f$. What is heard by the observer?

Oct/Nov 2022

A toy drone produces a sound with constant frequency $800\,\text{Hz}$. The speed of sound in air is $330\,\text{m s}^{-1}$. The drone travels in a straight line directly towards an observer and then carries on in the same straight line directly away from the observer. The drone moves at constant speed. Calculate the velocity of the drone when the frequency of the sound detected by the observer is $850\,\text{Hz}$?

Oct/Nov 2023

A source of sound waves is travelling at a steady speed straight towards a stationary observer. The sound waves move at $340\,\text{m s}^{-1}$ and have a frequency of $480\,\text{Hz}$. The observer detects sound waves with frequency $650\,\text{Hz}$. What is the speed of the source?

Oct/Nov 2023

A loudspeaker produces sound with frequency $f_s$. The loudspeaker is fitted to a car that travels straight towards a stationary observer and its speed is increasing. Which statement gives the frequency of the sound heard by the observer?

Oct/Nov 2023

A train moves at a constant high speed on a straight horizontal track towards an observer who is standing beside the track, as illustrated in Fig. 5.1. From $t = 0$ until it is well beyond the observer at time $t = t_2$, the train keeps sounding its horn continuously. The train goes past the observer at $t = t_1$. The horn produces a sound wave with constant frequency $f_s$.

Oct/Nov 2023

A train moves at constant speed along a straight horizontal track towards an observer who is standing next to the track, as shown in Fig. 6.1. As it nears the observer, the train’s horn is sounded continuously. The horn produces a sound with constant frequency $251\,\text{Hz}$. The frequency heard by the observer is $291\,\text{Hz}$. The speed of sound in air is $340\,\text{m s}^{-1}$.

Oct/Nov 2023

A source of sound sends out waves with a fixed frequency. Relative to a stationary observer, the source travels in a straight line at a constant speed. Which source velocity produces the lowest observed frequency?

Oct/Nov 2024

A source of sound waves with a constant frequency is moving as shown. In which case would the stationary observer hear a sound of the lowest frequency?

Oct/Nov 2024