Question

An operator sitting in his base camp sends a sound signal of frequency 400 Hz. The signal is reflected back from a car moving towards him. The frequency of the reflected sound is found to be 410 Hz. Find the speed of the car. Speed of sound in air = 324 m s−1

Answer 1

Speed of Car is 4 $ms^-^1$

Explanation:

• The signal received by the car is given by,

$f_r_e_f = \frac {v + v_0}{v}f_0$

• This signal is reflected back. So,

$f = \frac {v}{v + v_s} f_r_e_f$

• But in both cases the moving object is the car. So, vs=vo=u

So,

f = $\frac {v + u}{v - u} f_0$

410 = $\frac {324 + u}{324 - u} \times 400$

$\frac {41}{40} = \frac {324 + u}{324 - u}$

u = $\frac {648}{2 \times 81}$

= 4 $ms^-^1$