Speed of sound on a moving train

[Adithyan]

Homework Statement

Two trains A and B are moving with speed 20m/s and 30m/s respectively in the same direction on the same straight track with B ahead of A. The engines are at the front ends. The engine of trains A blows a long whistle.

Assume that the speed of sound of whistle is composed of components varying in frequency from f₁=800Hz to f₂=1120 Hz as shown in the figure. The spread in the frequency (ie, highest frequency - lowest frequency) is thus 320 Hz. The speed of sound in air is 340m/s.

Find the speed of the whistle for passengers in A and passengers in B

Homework Equations

The Attempt at a Solution

Relative velocity between A and B=10m/s. So speed of sound for passengers in B would be 10m/s less than 340m/s i.e, 330m/s and for people in A the speed of sound would be 340m/s.
But my answer is wrong. The answer is 360m/s for people in A and 310m/s for people in B. I could not think of a possible explanation. Can anyone help?

 

[phinds]

Since the trains are pulling apart, the separation speed ADDS to the speed of sound from the reference point of the passenger on the train (B) that did not blow its whistle. Why did you think it would subtract?

Your statement that "speed of sound for passengers in B would be ... " is incorrect. The speed of sound is the same for both sets of passengers. What is not the same is the speed of the THE sound FROM THAT WHISTLE. Maybe that's how you are confusing yourself.