a person leaning over a 126 m deep well accidentally drops a siren emitting soun

Question

a person leaning over a 126 m deep well accidentally drops a siren emitting sound of frequency 2450 hz. Just before this siren hits the bottom of the well, find the frequency and wavelength of the sound the person hears. (A) Just before this siren hits the bottom of the well, find the frequency of the sound the person hears coming directly from the siren? (B) Just before this siren hits the bottom of the well, find the wavelength of the sound the person hears coming directly from the siren. (C) Just before this siren hits the bottom of the well, find the frequency of the sound the person hears reflected off the bottom of the well. (D) Just before this siren hits the bottom of the well, find wavelength of the sound the person hears reflected off the bottom of the well. (E) What beat frequency does this person perceive?

Explanation / Answer

speed at tha bottom of well ,v = sqrt(2gh) = sqrt(2*9.8*126) = 49.695 m/s speed of sound, c = 330 m/s frequency ,f = 2450 Hz a) f' = f(c/c+v) = 2450*(330/(330+49.695)) = 2129.34 Hz b) wavelength = c/f' = 330/2129.34 = .1549776 m c) f' = f(c/c-v) = 2450*(330/(330-49.695)) = 2884.36 Hz d) wavelength = c/f' = 330/2884.36 = .11441013 m e) beat frequency = f2 -f1 = 2884.36 - 2129.34 = 755 Hz (approx)

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