Doppler Effect for Sound Waves (Cambridge (CIE) AS Physics): Exam Questions

A police car siren emits a sound wave with a frequency f_s of 440 Hz. The car is travelling away from an observer at a speed of 30 m s⁻¹.

The speed of sound is 340 m s⁻¹.

Which of the following is the frequency the observer hears?

Figure 1.1 shows object P, moving at velocity v_s. It emits a sound wave of frequency f_s. The speed of sound is v.

Fig. 1.1

At which point on the diagram will the observed frequency be $\frac{f_{s}v}{v+v_s}$?

A source moving at constant velocity v_s, emits a sound wave of frequency 450 Hz. A stationary observer records a frequency of 300 Hz.

What is the value of v_s, and is it moving towards or away from the observer?

Speed of sound, v = 340 m s^-1

A car of terrified observers try to get the car to start to drive away from a hungry T. rex, running toward them at a speed of 10 m s⁻¹. They hear the roar of the T. rex at a frequency of 170 Hz. The speed of sound in air is 340 m s⁻¹.

What is the frequency of the sound as emitted by the T. rex?

A car travels in a straight line towards a stationary observer at a speed of 0.2v, where v is the speed of sound. The car's horn emits a pure sound of frequency f_s.

What is the frequency of the sound of the horn as heard by the observer, f₀?

Two runners, A and B, run past each other in opposite directions, both at speed u. A police car has its siren on. It is traveling at a speed of 10u, in the same direction as Runner A. Runner A and Runner B observe the sound wave from the siren at frequencies of f_A and f_B respectively. The speed of sound is v.

What is the ratio of $\frac{f_A}{f_B}$?

Fig. 1.1 is a graph of the observed wavelength against time of a sound wave emitted from a single source. The emitted sound wave has a frequency $f_s$. The sound travels at a constant velocity directly towards an observer and a frequency of $f_T$ is observed. It then travels directly away from the observer and a frequency of $f_A$ is observed.

Fig. 1.1

What is the value of the ratio$\frac{f_A}{f_T}$?

Fig 1.1 is a diagram of a source that has a mass of 500 g and is connected to a rope of length 20 cm. The rope is attached to point Q and has a tension of 800 N. The source travels around point Q anticlockwise in a circular path with a velocity of v_s. It emits a sound wave of frequency f_s. When the source is at point P, an observer stands directly in line to the direction of motion at point O.

Fig 1.1

What is the value of v_s and $\frac{f_o}{f_s}$ when the source is at point P?

Speed of sound, v = 340 m s^-1

A source moves directly in line with an observer at a constant velocity v_s and emits a sound wave with a wavelength of λ_s. The observed wavelength of the source is λ₀ and the ratio $\frac{{\lambda }_0}{{\lambda }_s}$ is equal to $\frac{5}{4}$.

What is the value of v_s?

Speed of sound, v = 340 m s^-1