A sound source is moving towards stationary listener with 1/10th of the speed of sound. The ratio of apparent to real frequency is:
Correct answer: D. 10/9
- A. 11/10
- B. [11/10]-2
- C. [9/10]-2
- D. 10/9
Explanation
When a sound source is moving towards a stationary listener, the frequency of the sound appears higher to the listener compared to the actual frequency of the source. This is known as the Doppler effect. The ratio of the apparent frequency (f') to the real frequency (f) can be calculated using the following formula: f' / f = (v + v₀) / (v + vᵢ) Where: - f' is the apparent frequency - f is the real frequency - v is the speed of sound in the medium - v₀ is the velocity of the listener - vᵢ is the velocity of the source In this case, the source is moving towards the listener with 1/10th of the speed of sound. So, vᵢ = 1/10 * v. The listener is stationary, so v₀ = 0. Plugging these values into the formula, we get: f' / f = (v + v₀) / (v + vᵢ) = (v + 0) / (v + 1/10 * v) = v / (v + 1/10 * v) = v / (11/10 * v) = 10/11 Therefore, the ratio of the apparent frequency to the real frequency is 10/11, which is equivalent to 9/10.
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Progressive waves transfer energy through oscillations, with wavelength, frequency, amplitude and wave speed related by v = fλ; sound speed depends on the medium. Superposition produces interference and stationary waves in strings and organ pipes, while simple harmonic motion describes the oscillation itself and must be distinguished from wave propagation.
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