Question

A sound source from a motionless train emits a sinusoidal wave with a source frequency of fs = 514 Hz. Given that the speed of sound in air is 340 m/s and that you are a stationary observer. Find the wavelength of the wave you observe
(i) When the train is at rest
(ii) When the train is moving towards you at 15 m/s
(iii) When the train is moving away from you at 15 m/s

Answer 1

Answer:

i) 0.66 m

ii) 0.63 m

iii) 0.69 m

Hope this helps !

Answer 2

Answer:

The wavelength:

i.  0.662 meters.

ii. 0.690 meters.

iii. 0.632 meters.

Explanation:

The wavelength of a sound wave is given by the formula λ = v/f, where λ is the wavelength, v is the speed of sound, and f is the frequency of the wave.

(i) When the train is at rest, the speed of sound in air is 340 m/s. Therefore, the wavelength of the wave observed by the stationary observer is λ = 340/514 = 0.662 meters.

(ii) When the train is moving towards the observer at 15 m/s, the effective speed of the wave is the sum of the speed of sound and the speed of the train, i.e., 340 + 15 = 355 m/s. Therefore, the wavelength of the wave observed by the observer is λ = 355/514 = 0.690 meters.

(iii) When the train is moving away from the observer at 15 m/s, the effective speed of the wave is the difference between the speed of sound and the speed of the train, i.e., 340 - 15 = 325 m/s. Therefore, the wavelength of the wave observed by the observer is λ = 325/514 = 0.632 meters.

In summary, the wavelength of a sound wave observed by a stationary observer changes when the source or observer is in motion. When the source is moving towards the observer, the wavelength increases, and when the source is moving away from the observer, the wavelength decreases.

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