The driver of car travelling with a speed 30 meter/sec....

The driver of car travelling with a speed 30 meter/sec. towards a hill sounds 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 [MP PMT $\mathbf{1 9}$ (a) $720 \mathrm{~Hz}$ (b) $555.5 \mathrm{~Hz}$ (c) $550 \mathrm{~Hz}$ (d) $500 \mathrm{~Hz}$

The driver of car travelling with a speed 30 meter/sec. towards a hill sounds 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 [MP PMT $\mathbf{1 9}$
(a) $720 \mathrm{~Hz}$
(b) $555.5 \mathrm{~Hz}$
(c) $550 \mathrm{~Hz}$
(d) $500 \mathrm{~Hz}$

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Key Concepts

Successive Doppler Shifts

In scenarios where the sound undergoes two stages of Doppler shifting—first when the moving source emits sound towards a stationary reflector and then when the reflected sound is received by the moving source—the overall observed frequency is affected by both shifts. The combined effect can be calculated by applying the Doppler formula twice, accounting for the changing relative velocities in each stage.

Doppler Effect

The Doppler effect is a phenomenon that describes how the observed frequency of a wave changes when there is relative motion between the source and the observer. When the source and observer move closer together, the observed frequency increases, and when they move apart, it decreases. This effect is fundamental in wave mechanics and applies to all types of waves, including sound and light.

Reflection of Sound

Sound reflection occurs when sound waves hit a surface and bounce back. For a stationary reflector, the reflected wave retains the same frequency as received by the surface. However, if the source or the observer is moving, the Doppler effect comes into play during the emission and reception stages, altering the perceived frequency.

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