The frequency of an ambulance siren is 700 Hz. What are the frequencies heard by a stationary pedestrian

Question

The frequency of an ambulance siren is 700 Hz. What are the frequencies heard by a stationary pedestrian as the ambulance approaches and moves away from her at a speed of 90.0 km/h. (assume that the air temperature is 20 degrees C)

Answer 1

Doppler shift:

For an object moving toward you, the frequency you hear goes up:

f' = f * c / (c-v)

They give you the source frequency, f, and the speed of the source, v.  Look up the speed of sound at the given temperature.

When the ambulance is moving away, flip the minus sign in front of the v so the frequency is doppler shifted down instead of up.

Here's a formula you can use to get the speed of sound in air for a given temperature:

http://en.wikipedia.org/wiki/Speed_of_so...

Answer 2

The equation for the observed frequency of sound when the source is traveling toward you is: fo = fv/(v − vt),  where

fo is the observed frequency

f is the actual (emitted) frequency

v is the velocity of sound

vt is the velocity of the source toward you

When the source is travelling away from you the same equation is used but vt is negative. (This equation doesn't apply for sources travelling at or greater than the speed of sound.)

1) When the ambulance is approaching the observer:

f = 700 Hz

v = 343 m/s  (speed of sound in air at 20°C)

vt = 90 Km/h = 25 m/s

So, fo = 700*343/(343 - 25) = 755.031 Hz

2) At the moment the ambulance is passing the observer:

f = 700 Hz

v = 343 m/s

vt = 0

So, fo = fv/(v - 0) = f = 700Hz

3) And when the ambulance is moving away:

f = 700 Hz

v = 343 m/s

vt = -90 Km/h = -25 m/s

So, fo = 700*343/(343 + 25) = 652.446Hz

Hence, the frequences as amulance approaches, passes, and moves away from the observer are respectively: 755.031Hz, 700Hz, and 652.446Hz.