Question

An aircraft is moving away from you at half the speed of sound, which, on that day is about 340 m/s. The jet engines make a sound that is primarily about 300 Hz. What is the apparent frequency of the jet engines?

(A) 150 Hz
(B) 200 Hz
(C) 470 Hz
(D) 600 Hz

Answer 1

Concept:

Doppler Effect :- The Doppler Effect is the apparent change in frequency due to the relative motion between the observer and the source of sound.

Given:

Speed of sound, $v_{s}$ = 340 m/s

Frequency of sound at the source, $f_{o}$ = 300 Hz

Speed of aircraft, $v_{o}$ = half of speed of sound = 340/2 = 170 m/s

Find:

Apparent frequency of the jet engines.

Step-by-step explanation:

Step 1 - According to the doppler effect, we have

                         $f = \frac{f_{o}v_{s} }{v_s+v_o}$       -----------   (i)

where f = apparent frequency of the jet engine

           $f_o$ = frequency of sound at the source

           $v_s$ = speed of sound

           $v_o$ = speed of source (aircraft)

(+) sign in the denominator tells us that source is moving away from the listener.

Step 2 - Putting the values in equation (i), we get

$f = \frac{300X340}{340+170}$

$f = \frac{102000}{510}$

$f = 200 Hz$

Step 3 - Hence, the apparent frequency of the jet engines = f = 200 Hz.

Answer:

Option (B) 200 Hz is the correct answer.

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