Question

Figure 3 shows an emitter and receiver of waves mounted in the same location on a control tower. This device is used to measure the speed of a moving target that moves directly towards the control tower, by analyzing the frequency of the reflected waves from the moving target. Express the speed of the object V_O as a function of emitter frequency f_E and the reflected wave frequency f_R. Suppose f_E = 18.0KHz, f_R = 22.2 KHz and sound speed in air is 343m/s. Find V_O. Will wind affect the result of the measurement?

Answer 1

This is a doppler effect problem where receiver is moving and emitter is moving relative to target with velocity v₀.

So

$f_r=f_e\left(\frac{c+v_0}{c-v_0}\right)\\ \implies f_r c-f_rv_0=f_ec+f_ev_0\\ \implies \frac{(f_r-f_e)c}{f_r+f_e}=v_0$

$\frac{(f_r-f_e)c}{f_r+f_e}=v_0\\ \implies \frac{(22.2-18)\times 10^3\times 343}{(22.2+18)\times 10^3}=v_0\\ \implies 35.84/s=v_0$

Generally wind affects measurement.