Question

The apparent frequency of the whistle of an engine changes in the ratio 9:8 as the engine passes a stationary observer. If the velocity of the sound is 340 ms⁻¹, then the velocity of the engine is:

A 20 m/s
B 180 m/s
C 40 m/s
D 340 m/s

Answer 1

The apparent frequency of the whistle of an engine changes as it passes a stationary observer due to the Doppler effect. By using the Doppler effect equation and the given information, we find that the velocity of the engine is approximately 40 m/s. Thus, the correct answer is C, 40 m/s.

Step-by-step explanation:

The problem described involves the Doppler effect, which is a change in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source. We can use the Doppler effect equation to solve this problem:

f' = f (v + vo) / (v - vs)

Where:

• f' is the apparent frequency
• f is the actual frequency
• v is the speed of sound
• vo is the speed of the observer (0 in this case since the observer is stationary)
• vs is the speed of the source (in this case, the engine)

Given that the ratio of the apparent frequency to the actual frequency is 9:8, we can set up the following equation:

9/8 = (v + 0) / (v - vs)

Since the velocity of sound, v, is given as 340 m/s, we can solve for the velocity of the engine, vs:

9/8 = 340 / (340 - vs)

Multiplying both sides by (340 - vs) and then by 8/9 to isolate vs gives:

vs = 340(1 - 8/9)

vs = 340/9

vs = 37.78 m/s (approximately 40 m/s)

Hence, the correct answer is C, which is 40 m/s.