Question

What frequency (in Hz) is received by a person watching an oncoming ambulance moving at 116 km/h and emitting a steady 950 Hz sound from its siren? The speed of sound on this day is 345 m/s.

Answer 1

To solve this problem we will apply the concepts related to the Doppler Effect, defined as the change in apparent frequency of a wave produced by the relative movement of the source with respect to its observer. Mathematically it can be written as

$f_{obs} = f(\frac{v_w}{v_w-v_s})$

Here,

$f_s$= Frequency of the source

$v_w$ = Speed of the sound

$v_s$= Speed of source

Now the velocity we have that

$v_s = 116km/h (\frac{1000m}{1km})(\frac{1h}{3600s})$

$v_s = 32.22m/s$

Then replacing our values,

$f_{obs} = (950Hz) (\frac{345m/s}{345m/s-32.22m/s})$

$f_{obs} = 1047.86Hz$

Therefore the frequency of the observer is 1047.86Hz