Question

The security alarm on a parked car goes off and produces a frequency of 960 Hz. The speed of sound is 343 m/s. As you drive toward this parked car, pass it, and drive away, you observe the frequency to change by 75 Hz. At what speed are you driving

Answer 1

Answer: $13.4\ m/s$

Explanation:

Given

The frequency of the source is $f_o=960\ Hz$

Change in frequency is $75\ Hz$

Speed of sound $c=343\ m/s$

Suppose $v$ is the velocity of the observer

Doppler frequency is given by

$f'=f_o\left(\dfrac{c\pm v_o}{c\pm v_s}\right)$

Here, the source is at rest

While approaching source, frequency is

$f_1=f_o\left(\dfrac{c+v}{c}\right)\quad \ldots(i)$

While leaving, frequency is

$f_2=f_o\left(\dfrac{c-v}{c}\right)\quad \ldots(ii)$

The difference in the frequency is

$\Rightarrow f_1-f_2=75\\\\\Rightarrow f_o\left(\dfrac{c+v}{c}\right)-f_o\left(\dfrac{c-v}{c}\right)=75\\\\\Rightarrow f_o\left(\dfrac{2v}{c}\right)=75\\\\\Rightarrow v=\dfrac{75\times 343}{2\times 960}\\\\\Rightarrow v=13.39\approx 13.4\ m/s$