The driver of a car traveling with speed 30 m / s towards a hill sound a horn of frequency 600

step 1 In this question we have given that the driver of a car traveling with speed of 30 meter per sec

The driver of a car traveling with speed 30 m / s towards a...

The driver of a car traveling with speed $30 \mathrm{~m} / \mathrm{s}$ towards a hill sound a horn of frequency $600 \mathrm{~Hz}$. If the velocity of sound in air is $330 \mathrm{~m} / \mathrm{s}$, the frequency of reflected sound as heard by the driver is (A) $720 \mathrm{~Hz}$ (B) $555.5 \mathrm{~Hz}$ (C) $550 \mathrm{~Hz}$ (D) $500 \mathrm{~Hz}$

The driver of a car traveling with speed $30 \mathrm{~m} / \mathrm{s}$ towards a hill sound a horn of frequency $600 \mathrm{~Hz}$. If the velocity of sound in air is $330 \mathrm{~m} / \mathrm{s}$, the frequency of reflected sound as heard by the driver is
(A) $720 \mathrm{~Hz}$
(B) $555.5 \mathrm{~Hz}$
(C) $550 \mathrm{~Hz}$
(D) $500 \mathrm{~Hz}$

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Key Concepts

Doppler Effect

The Doppler effect refers to the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source. It explains why a sound appears higher in pitch as the source approaches and lower as it recedes. This concept is fundamental in understanding the shifts observed in various wave phenomena, including sound and light waves.

Moving Source and Observer Dynamics

When applying the Doppler effect, it is crucial to consider the relative motion of both the source and the observer. Whether the source is moving towards a stationary observer or vice versa, the effective velocity of the approach or separation influences the observed frequency. This principle is essential in calculating the frequency changes seen by either party in a setting where one or both are in motion.

Reflection of Sound Waves

In scenarios where sound waves are reflected, the reflecting surface acts as a secondary source of sound. The process involves the initial Doppler shift as the sound approaches the surface followed by another shift when the reflected sound is received by a moving observer. This double application of the Doppler effect is key in analyzing the overall frequency change in reflected sound problems.

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