[Maximum number: 3]

A student investigates the sound from a horn attached to a car, as shown in Fig. 2.1.

Fig. 2.1 (not to scale)

A microphone is placed at the side of the road and connected to a frequency meter. The car travels towards the microphone. The frequency f of the sound detected by the microphone is read from the frequency meter.

The speed of the car is measured by two speed detectors. The two measurements of speed are $v_{1}$ and $v_{2}$ . The average speed v of the car is determined from $v_{1}$ and $v_{2}$ .

The experiment is repeated for different speeds of the car.
It is suggested that f and v are related by the equation

f=\frac{f_{\mathrm{s}} k}{k-v}

where $f_{\mathrm{s}}$ is the frequency of the sound emitted by the horn and k is a constant.

(a)

A graph is plotted of $\frac{1}{f}$ on the y-axis against v on the x-axis.

Determine expressions for the gradient and y-intercept.

\begin{array}{r} \text { gradient }= \\ y \text {-intercept }= \end{array}

[ 1 ]

(b)

(i)

Using your answers to (a), (c)(iii) and (c)(iv), determine the values of $f_{\mathrm{s}}$ and k. Include appropriate units.

\begin{gathered} f_{\mathrm{s}}= \\ k= \end{gathered}

[ 2 ]

[Maximum number: 1]

A man stands stationary in front of a swing. A child sits and swings.

The child blows a whistle that emits a sound at a constant frequency.
The man observes the frequency of the sound when the swing is at positions X, Y and Z .
When will the man hear the highest frequency?

when the swing is at X

when the swing is at Y and moving away from the man

when the swing is at Y and moving towards the man

when the swing is at Z

[Maximum number: 1]

The warning signal on an ambulance has a frequency of 600 Hz . The speed of sound is $330 \mathrm{~ms}^{-1}$ . The ambulance is travelling with a constant velocity of $25 \mathrm{~ms}^{-1}$ towards an observer. The ambulance passes, and then moves away from the observer with no change in velocity.

Which overall change in observed frequency takes place between the times at which the ambulance is a long way behind the observer and when it is a long way in front of the observer?

49 Hz

84 Hz

91 Hz

98 Hz

[Maximum number: 1]

A loudspeaker emits sound of frequency $f_{\mathrm{s}}$ . The loudspeaker is attached to a car that moves with increasing speed directly towards a stationary observer.

Which statement describes the frequency of the sound heard by the observer?

a frequency greater than $f_{\mathrm{s}}$ and increasing

a frequency greater than $f_{\mathrm{s}}$ but decreasing

a frequency less than $f_{\mathrm{s}}$ and decreasing

a frequency less than $f_{\mathrm{s}}$ but increasing

[Maximum number: 1]

A source of sound waves is moving at a constant speed directly towards a stationary observer.
The sound waves have a speed of $340 \mathrm{~ms}^{-1}$ and a frequency of 480 Hz . The observer hears sound waves of frequency 650 Hz .

What is the speed of the source?

$89 \mathrm{~ms}^{-1}$

$120 \mathrm{~m} \mathrm{~s}^{-1}$

$250 \mathrm{~ms}^{-1}$

$340 \mathrm{~m} \mathrm{~s}^{-1}$

[Maximum number: 1]

A toy drone emits a sound of constant frequency 800 Hz . The speed of the sound in the air is $330 \mathrm{~m} \mathrm{~s}^{-1}$ .

The drone moves along a straight path directly towards an observer and then continues in a straight line directly away from the observer. The speed of the drone is constant.

What is the velocity of the drone when the frequency of the sound heard by the observer is 850 Hz ?

magnitude of

velocity $/ \mathrm{m} \mathrm{s}^{-1}$

direction of velocity

away from the observer

towards the observer

[Maximum number: 1]

A vehicle moves with constant velocity along a road directly towards an observer. The observed frequency of the sound from the vehicle changes as the vehicle moves past the observer.

Which phenomenon explains the change in frequency?

diffraction

interference

polarisation

the Doppler effect

[Maximum number: 1]

A source X emits a sound wave of constant frequency f.
The wave is subsequently received at a stationary detector Y .
The frequency of the wave that is detected by Y is less than f.
What could be the reason for this?

Between X and Y, the wave undergoes diffraction.

Between X and Y, the wave undergoes reflection.

X is moving away from Y .

X is moving towards Y .

[Maximum number: 1]

A car travels at a constant speed along a straight line PQ .
A loudspeaker attached to the car emits sound of constant frequency f. A stationary observer is at point O.

What does the observer hear as the car moves from P towards Q ?

a frequency less than f that decreases as the car moves from P towards Q

a frequency less than f that increases as the car moves from P towards Q

a frequency more than f that decreases as the car moves from P towards Q

a frequency more than f that increases as the car moves from P towards Q

[Maximum number: 1]

An observer hears a sound wave emitted from a moving source.
The observed frequency is less than the frequency of sound emitted from the source.
What could be the reason for this?

The source is moving away from the observer.

The source is moving towards the observer.

The speed of the sound wave in air decreases due to the movement of the source.

The speed of the sound wave in air increases due to the movement of the source.