An ambulance is speeding towards you at 20 m/s. If the siren is producing a sound at a frequency of 737 Hz, what is the frequency you hear? (The speed of sound is 343 m/s).

828 Hz

Explanation:

The Doppler effect equation states:  

fr = (c + vr) / (c + vs) fs,  

where fr is the frequency heard by the receiver,  

c is the speed of sound,  

vr is the velocity of the receiver,  

vs is the velocity of the source,  

and fs is the frequency emitted at the source  

One important note: vr is positive if the receiver is moving towards the source, negative if away.  

Conversely, vs is positive if the receiver is moving away from the source, and negative if towards.

The ambulance is moving toward you, so vr is positive and vs is negative.

Plugging values into the equation:

fr = (343 m/s + 20 m/s) / (343 m/s − 20 m/s) (737 Hz)

fr = 828 Hz

As you would expect from the Doppler effect, you hear a higher frequency when the ambulance is moving toward you.

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