Two golf carts have horns that emit sound with a frequency of 394 Hz. The golf carts are traveling toward one another, each traveling with a speed of 9.5 m/s with respect to the ground. If one of the drivers sounds her horn, what frequency does the other driver hear? The speed of sound at the golf course is 345 m/s.
A)378 Hz
B)394 Hz
C)408 Hz
D)416 Hz
E)424 Hz

Question

Quizplus · Accepted Answer

First, we need to calculate the relative velocity of the golf carts: since they are traveling towards each other, their relative velocity is the sum of their individual velocities, which is 19 m/s (9.5 m/s + 9.5 m/s).

Next, we can use the formula for the Doppler effect:

f' = f((v + vd) / (v + vs))

where:
f = frequency emitted by the source
v = speed of sound in the medium (345 m/s)
vd = velocity of the detector (in this case, the other golf cart) relative to the medium (i.e., the speed of the detector as seen by someone standing on the ground would be the relative velocity we calculated earlier, but we need to take into account that the medium itself is also moving, so we need to add the speed of the medium as well)
vs = velocity of the source (in this case, the golf cart that is sounding the horn)

Plugging in the values, we get:

f' = 394 ((345 + 19) / (345 + 9.5))
f' ≈ 416 Hz

Therefore, the other driver hears a frequency of approximately 416 Hz. The correct answer is D.

Two Golf Carts Have Horns That Emit Sound with a Frequency