Loudspeaker A is switched off. Loudspeaker B moves away from M at a speed of 1.5 m s⁻¹ while emitting a frequency of 3.0 kHz.

Determine the difference between the frequency detected at M and that emitted by B.

A train moving at speed u relative to the ground, sounds a whistle of constant frequency f as it moves towards a vertical cliff face.

The sound from the whistle reaches the cliff face and is reflected back to the train. The speed of sound in stationary air is c.

What whistle frequency is observed on the train after the reflection?

A.  $\frac{(c+u)}{(c-u)}f$

B.  (c + u)f

C.  (c – u)f

D.  $\frac{(c-u)}{(c+u)}f$

A stationary sound source emits waves of wavelength $\lambda$ and speed v. The source now moves away from a stationary observer. What are the wavelength and speed of the sound as measured by the observer?

The wavelength of the light in the beam when emitted by the galaxy was 621.4 nm.

Explain, without further calculation, what can be deduced about the relative motion of the galaxy and the Earth.

The motion sensor operates by detecting the sound waves reflected from the base of the mass. The sensor compares the frequency detected with the frequency emitted when the signal returns.

The sound frequency emitted by the sensor is 35 kHz. The speed of sound is 340 m s⁻¹.

Determine the maximum frequency change detected by the sensor for test 2.

Police use radar to detect speeding cars. A police officer stands at the side of the road and points a radar device at an approaching car. The device emits microwaves which reflect off the car and return to the device. A change in frequency between the emitted and received microwaves is measured at the radar device.

The frequency change Δf is given by

$$\mathrm{\Delta }f=\frac{2fv}{c}$$

where f is the transmitter frequency, v is the speed of the car and c is the wave speed.

The following data are available.

(i) Explain the reason for the frequency change.

(ii) Suggest why there is a factor of 2 in the frequency-change equation.

(iii) Determine whether the speed of the car is below the maximum speed allowed.

An ambulance siren emits a sound of frequency 1200 Hz. The speed of sound in air is 330 m s^–1. The ambulance moves towards a stationary observer at a constant speed of 40 m s^–1. What is the frequency heard by the observer?

A.   $\frac{1200\times 330}{370}$Hz

B.   $\frac{1200\times 290}{330}$Hz

C.   $\frac{1200\times 370}{330}$Hz

D.   $\frac{1200\times 330}{290}$Hz

A train is approaching an observer with constant speed

                                                         $$\frac{c}{34}$$

where c is the speed of sound in still air. The train emits sound of wavelength λ. What is the observed speed of the sound and observed wavelength as the train approaches?

A train is moving in a straight line away from a stationary observer when the train horn emits a sound of frequency $f_0$. The speed of the train is $0.10v$ where $v$ is the speed of sound. What is the frequency of the horn as heard by the observer?

A.  $\frac{0.9}{1}{f}_0$

B.  $\frac{1}{1.1}{f}_0$

C.  $\frac{1.1}{1}{f}_0$

D.  $\frac{1}{0.9}{f}_0$

Calculate $v$.

Sound of frequency 2400 Hz is emitted from a stationary source towards the oscillating plate in (b). The speed of sound is 340 m s⁻¹.

Determine the maximum frequency of the sound that is received back at the source after reflection at the plate.