A car blowing its horn at 480 Hz moves towards a high wall at a speed of 20 m / s. If the spee

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A car blowing its horn at 480 Hz moves towards a high wall...

A car blowing its horn at $480 \mathrm{~Hz}$ moves towards a high wall at a speed of $20 \mathrm{~m} / \mathrm{s}$. If the speed of sound is $340 \mathrm{~m} / \mathrm{s}$, the frequency of the reflected sound heard by the driver sitting in the car will be closest to $\ldots \ldots \ldots . \mathrm{Hz}$ (A) 510 (B) 524 (C) 568 (D) 480

Key Concepts

Frequency Calculation in Relative Motion

Calculating the frequency alteration due to the Doppler Effect typically involves formulas that relate the observed frequency to the emitted frequency, the speed of the wave, and the relative speeds of the source and receiver. When dealing with reflections and double Doppler shifts, successive applications of these formulas are needed. This approach helps in precisely determining the frequency observed in cases where there is relative motion between the sound source, the reflecting surface, and the receiver.

Doppler Effect

The Doppler Effect is a phenomenon where the observed frequency of a wave changes due to the relative motion between the source and the observer. When the source and observer move towards each other, the observed frequency increases, and when they move apart, it decreases. This effect is commonly applied to sound waves and is crucial in understanding how motion alters the perception of wave frequencies.

Reflection of Sound and Doppler Shift

When a sound wave reflects off a surface, the reflected wave can undergo a Doppler shift if either the source or the receiver is moving relative to the reflecting surface. In this scenario, the surface (e.g., a wall) acts as a stationary reflector, causing the sound to experience a Doppler shift twice: once when the wave approaches the reflector and again when it is received by the moving observer after reflection. This double shift significantly alters the frequency heard by the receiver.

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