BridgeWavesFree

Siren on State Highway 1

Doppler (sound and light, moving observer/source, circular)

An ambulance travels at constant speed

v_{\text{s}}

along a straight stretch of State Highway 1 near Ōtaki with its siren emitting a steady frequency

f

. A cyclist stopped on the shoulder, very close to the edge of the road, hears

f_{\text{a}} = 742\ \text{Hz}

while the ambulance approaches and

f_{\text{r}} = 618\ \text{Hz}

after it has passed. The air is still and the speed of sound is

v = 343\ \text{m s}^{-1}

(a)

explain2 marks

Using a description of the wavefronts, explain why the cyclist hears a higher frequency while the ambulance approaches, even though the siren's frequency does not change.

(b)

show that2 marks

Show that the speed of the ambulance is given by

v_{\text{s}} = v\dfrac{f_{\text{a}} - f_{\text{r}}}{f_{\text{a}} + f_{\text{r}}}

(c)

calculate2 marks

Calculate the speed of the ambulance (in m s⁻¹ and km h⁻¹) and the frequency actually emitted by the siren. Explain why the emitted frequency is not the average of

742\ \text{Hz}

and

618\ \text{Hz}

, even though the ambulance's speed is the same before and after it passes.

(d)

sketch2 marks

Sketch, on one set of axes, graphs of the frequency heard against time as the ambulance passes (i) the cyclist on the road edge and (ii) a walker standing

30\ \text{m}

from the road. Explain the difference in shape, and state the frequency each listener hears for the sound emitted when the ambulance is at its closest point to them.

Your score: 0 / 8(0 of 4 parts marked — open “Mark it” on each part)