A source of sound and a listener are both moving in the same direction, the source following the listener. If the respective velocities of sound, source, and listener are vr, vs , and vl , then the ratio of the actual frequency of the source and the apparent frequency as received by the listener is:
Correct answer: C. (V-Vs)/(V-Vl)
- A. (V-Vl)/ (V-Vs)
- B. V+Vl)/ (V+Vs)
- C. (V-Vs)/(V-Vl)
- D. (V+Vs)/( V+Vl)
Explanation
The Doppler effect formula for frequency is f′=v±v/s v±vr ×f, where f′ is the apparent frequency, f is the actual frequency, vr is the velocity of the receiver (listener), and vs is the velocity of the source. Here, both source and listener move, but the listener is following the source. Hence, vr =vl . Therefore, the correct ratio is (c) (V-Vs)/(V-Vl)
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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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