Question

Two train whistles, and , each have a frequency of 392 Hz. is stationary and is moving toward the right (away from ) 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 (). No wind is blowing. (a) What is the frequency from as heard by the listener? (b) What is the frequency from as heard by the listener? (c) What is the beat frequency detected by the listener?

Answer 1

Answer:

Part a)

f = 371.1 Hz

Part b)

f = 417.7 Hz

Part c)

beat frequency = 46.6 Hz

Explanation:

Part a)

Due to doppler's Effect the frequency of the sound heard by the train which is moving away from the observer is given as

$f_1 = f_0\frac{v + v_o}{v + v_s}$

$f_1 = 392(\frac{340 + 15}{340 + 35})$

$f_1 = 371.1 Hz$

Part b)

Now from the second train which is approaching the person we can say

$f_2 = f_0\frac{v - v_o}{v - v_s}$

$f_2 = 392(\frac{340 - 15}{340 - 35})$

$f_2 = 417.7 Hz$

Part c)

As we know that beat frequency is the difference in the frequency from two sources

$f_b = f_2 - f_1$

$f_b = 417.7 - 371.1 = 46.6 Hz$