Question

A stationary siren creates an 894 Hz
sound. When a motorcyclist is driving
toward it, she hears a 926 Hz sound
How fast is she driving?
(Speed of sound = 343 m/s)
(Unit = m/s)​

Answer 1

Answer:

12.3 m/s

Explanation:

The Doppler equation describes how sound frequency depends on relative velocities:

fr = fs (c + vr)/(c + vs),

where fr is the frequency heard by the receiver,

fs is the frequency emitted at the source,

c is the speed of sound,

vr is the velocity of the receiver,

and vs is the velocity of the source.

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.

Given:

fs = 894 Hz

fr = 926 Hz

c = 343 m/s

vs = 0 m/s

Find: vr

926 = 894 (343 + vr) / (343 + 0)

vr = 12.3

The speed of the car is 12.3 m/s.