Question

A flowmeter in the ocean sends a sound wave with the frequency of 75000 Hz and senses the frequency of reflection from a particle moving around in the ocean that is 75100 Hz.
a) What is the speed of said particle towards the flowmeter?
b) What if the particle had an audio sensor, what frequency would it measure?
Given is the speed of sound: 1440 m/s
c) The reflection from the particle comes at the flowmeter 0,02 seconds after the sound wave is sent from the flowmeter. What is the distance between the flowmeter and the particle?

Answer 1

v_sound = 1440 m/s

let v_particle is the particle's speed.

a) reflection frequency, f' = f*(v_sound + v_particle)/(v_sound - v_particle)

75100 = 75000*(1440 + v_particle)/(1440 - v_particle)

(1440 - v_particle)*75100 = 75000*(1440 + v_particle)

1440*75100 - v_particle*75100 = 75000*1440 + 75000*v_particle

1440*(75100 - 75000) = v_particle*(75000 + 75100)

==> v_particle = 1440*(75100 - 75000)/(75000 + 75100)

= 0.960 m/s

b) frequency experienced by the particle, f'' = f*(v_sound + v_particle)/v_sound

= 75000*(1440 + 0.96)/1440

= 75050 Hz

c) if t = 0.02 s

distance between sensor and the particle, d = t*c/2

= 0.02*1440/2

= 14.4 m

if t = 2s,

d = 2*1440/2

= 1440 m