Question

A noisemaker produces a constant sound of frequency fsfs=131.0Hz. It is dropped from rest down a well of height D and splashes into the water at the bottom. A listener at the top of the well hears the splash after t=6.8s have passed.

If the speed of sound in air is 343msms, what frequency fLfL does the listener hear from the noisemaker the instant before it hits the water? Answer in Hz.

Answer 1

let t1 is the time taken for the noice maker to reach the water.

use, D = (1/2)*g*t1^2

t1 = sqrt(2*D/g)

t1 = sqrt(2*D/9.8) ---(1)

time taken for the sound to reach from the water surface to top of the well,

t2 = D/v_sound

t2 = D/343

t1 + t2 = 6.8 s

sqrt(2*D/9.8) + D/343 = 6.8

==> D = 191 m

speed of noice maker when before hitting water, v = sqrt(2*g*D)

= sqrt(2*9.8*191)

= 61.2 m/s

frequency heard by the listener, f' = f*v_sound/(v + v_sound)

= 131*343/(61.2 + 343)

= 111 Hz <<<<<<<<<<----------------Answer