Two Train whistles, A and B each have a frequency of 408Hz. A is stationary and B is moving toward the right (away from A) at a speed of 35.0m/s. A listener is between the two whistles and is moving toward the right at a speed of 15.0m/s. What is the frequency from A and B as heard by the listener?

Answer 1

From an ancient reply:
fr = fs[(v-vd)/(v-vs)]

fs is the frequency of the source, relative to the medium carrying the waves. We assume that is also the speed with respect to the ground (no wind)

fr is the received frequency.
v is the speed of sound in the air.
vd is the speed of the detector (listener)away from the source
vs is the speed of the source towards the detector.

Two Train whistles, A and B each have a frequency of 408Hz. A is stationary and B is moving toward the right (away from A) at a speed of 35.0m/s. A listener is between the two whistles and is moving toward the right at a speed of 15.0m/s. What is the frequency from A and B as heard by the listener?

Using 340 m/s for v
First due to A
d moving away from A at 15 m/s
fr = 408 (340-15)/(340-0) = 390 Hz
Now dues to B
Vd = -15
Vs = -35
fr = 408(340+15)/(340+35) = 386 Hz