Question

Two loudspeakers emit 400Hz notes. One speaker sits on the ground. The other speaker is in the back of a pickup truck. You hear 7.00 beats per second as the truck drives away from you.

What is the trucks speed (m/s)?

Answer 1

This is a doppler frequency shift problem. The doppler equation for frequency is:

f = v*f0/(v + vs)

where "f" is the observed frequency, "f0" is the emitted frequency, "v" is the velocity of the air, and "vs" is the source velocity.

The "7 beats per second" (B) tells you that the frequency difference is 10Hz.

B = f0 - v*f0/(v + vs) = 7

I used the negative sign since the source is moving "away" from you.

(1 - v/(v+vs)) = 7/f0

(1 - 7/f0) = v/(v + vs)

(1 - 7/f0)*(v + vs) = v

(1 - 7/f0)*vs = v*(1 - (1 - 7/f0))

vs = v*(7/f0)/(1 - 7/f0) = 344*(7/400)/(1 - 7/400) = 6.1272 m/s