Question

Two train whistles, a and b, each have a frequency of 395 Hz. a is stationary and b is moving toward the right (away from a) at a speed of 35.0 m/s. A listener is between the two whistles and is moving toward the right with a speed of 15.0 m/s. What is the frequency from b as heard by the listener? Express your answer in hertz.

Answer 1

To find the frequency from whistle b as heard by the listener, the Doppler effect equation is applied, with appropriate signs for the velocities of the listener and the moving source.

Step-by-step explanation:

The Doppler effect is the observed change in frequency (or wavelength) of a wave in relation to an observer who is moving relative to the wave source. In the case of train whistles a and b both emitting a frequency of 395 Hz, and whistle b moving away at 35.0 m/s while the listener moves towards the right at 15.0 m/s, we can calculate the observed frequency from whistle b using the Doppler formula:

f' = f ∗ (v + Vo) / (v + Vs)

Here, f' is the observed frequency by the listener, f is the source frequency, v is the speed of sound in air (usually around 343 m/s at room temperature), Vo is the velocity of the observer moving towards the source, and Vs is the velocity of the source moving away from the observer. Since we are given that whistle b is moving away (to the right) in relation to the listener, and assuming the speed of sound is 343 m/s at room temperature, we use:

f' = 395 Hz ∗ (343 m/s + 15.0 m/s) / (343 m/s + 35.0 m/s)

Calculating gives the observed frequency from whistle b as heard by the listener, which is the answer to the problem.