The driver of a car travelling at a speed of towards a hill sounds a horn of frequency . If the velocity of sound in air is , the frequency of reflected sound as heard by the driver is:
Let the velocity of sound be , the velocity of the car be , and the actual frequency of the horn be . When the sound travels towards the hill, the car acts as a moving source approaching a stationary reflector (the hill). The apparent frequency received by the hill is: When the sound is reflected from the hill, the hill acts as a stationary source emitting frequency , and the car acts as an observer moving towards the source. The frequency heard by the driver is: Substituting into the second equation gives the formula for the apparent frequency of an echo heard by a moving source: Therefore, the driver hears a frequency of .
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