Question

A woman is sitting at a bus stop when an ambulance with a siren wailing at 317 Hz approaches at 69 miles per hour (mph). Assume the speed of sound to be 343 m/s. a) How fast is the ambulance moving in meters per second? (perform the necessary unit conversion) Vs= 69 mph = m/s b) What frequency does the woman hear? fa = Hz c) What speed (vs) would the ambulance be traveling in order for the woman to hear the siren at an approaching frequency of 350 Hz? Vs= m/s d) What frequency would she hear as the siren moves away from her at the same speed (as in part c)? fa = Hz

Answer 1

Answer:

a) va = 30.8457 m/s

b) fa = 348.3245 Hz

c) va = 32.3397 m/s

d) fa = 289.6869 Hz

Explanation:

Look at the solution in the attached Word file

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Answer 2

Answer:

a)30.67 m/s

b)348,12 Hz

c)32,34 m/s

d)289,69 Hz

Explanation:

a)

To convert 69 mph to m/s we have:

$69\times 1.6=110.4\, Km/h=\frac{110.4}{3.6}=30.67 \, m/s$

b)

For a resting receiver and an approaching source we have the following Doppler formula:

$f=f_0\frac{c}{c-v_s}$

where $v_s$ is the source, and c is the speed of sound, f the perceived frequency and $f_0$ the frequency as perceived by the source. Plugging all the relevant values we get:

$f=348,12 \, Hz$

c)

Using the same formula as above and solving for $v_s$ we have:

$v_s=c\frac{f-f_0}{f}=32,34 \, m/s$

d)

Now we have another Doppler formula for a source that is moving away from the receiver:

$f=f_0\frac{c}{c+v_s}=289.69 Hz$