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Question

A car moves with a speed of 54 km h−1 towards a cliff. The horn of the car emits sound of frequency 400 Hz at a speed of 335 m s−1. (a) Find the wavelength of the sound emitted by the horn in front of the car. (b) Find the wavelength of the wave reflected from the cliff. (c) What frequency does a person sitting in the car hear for the reflected sound wave? (d) How many beats does he hear in 10 seconds between the sound coming directly from the horn and that coming after the reflection?

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Solution

Given:
Velocity of car vcar = 54 kmh−1 = 54×518=15 ms-1
Frequency of the car f = 400 Hz
Velocity of sound in air vair = 335 ms−1
Wavelength in front of the car λ = ?

(a) Net velocity in front of the car v = vcar-vair = 335-15 = 320 m/s

As v=fλ, λ=vf
λ=320400=80 cm

(b) The frequency f1 heard near the cliff is given by:

f1=vairvair+vcar×f0f1=335335+5×400f1=335×400320 Hzf1=418.75 Hz

As we know,
v=fλ.

Wavelength reflected from the cliff is λ=vf1=335418.75=80 cm

(c) Here, v0 = 15 ms-1.

Frequency of the reflected sound wave f2 heard by the person sitting in the car:

f2=v+v0v×f1f2=335+15335×335320×400f2=437 Hz

(d) He will not hear any beat in 10 seconds because the difference of frequencies is greater than 10 (persistence of sound for the human ear is 1/10 of a second).

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