A police car with a siren of frequency $8$ kHz is moving with uniform velocity $36 \mathrm{km}\, \mathrm{hr}^{-1}$ towards a tall building which reflects the sound waves. The speed of sound in air is $320 \mathrm{m}\, \mathrm{s}^{-1}$. The frequency of the siren heard by the car driver is?

  • A: $8.50$ kHz
  • B: $8.24$ kHz
  • C: $7.75$ kHz
  • D: $7.50$ kHz
  • $\begingroup$ Welcome to Phys.SE please read Phys.SE Help Center, it says that: "Do my homework"-type physics questions shouldn't be asked here: "example: "A 4kg ball is traveling at 8m/s in the x direction, how do I find...". $\endgroup$
    – G B
    May 11, 2014 at 12:13
  • $\begingroup$ I asked my teacher he showed the solution and answer was option A but after i came back home i wasn't able to sove it again $\endgroup$ May 11, 2014 at 12:13
  • $\begingroup$ The general expression for the apparent frequency (n") produced due to Doppler effect is n"= n(v+w–vL)/(v+w–vS) where ‘v’ is the velocity of sound, ‘w’ is the wind velocity ‘vL’ is the velocity of the listener, ‘vS’ is the velocity of the source. of sound and ‘n’ is the actual frequency of the sound emitted by the source., i got upto this point. after that i am getting stucked., this question is also not a do my homework type question because it was in one of my senior's book. $\endgroup$ May 11, 2014 at 12:27
  • $\begingroup$ this is all what i have tried @GigiButbaia $\endgroup$ May 11, 2014 at 12:28
  • 1
    $\begingroup$ Actually the car driver hears two frequencies. First the sound he is moving with, second the reflected sound. $\endgroup$
    – KvdLingen
    May 11, 2014 at 12:38

1 Answer 1


So Police car is moving at $36$ $\mathrm{km/h}$ ($V_0$), The Frequency of siren is $8$ $\mathrm{kHz}$ ($f_0$) and speed of sound is $320$ $\mathrm{m/s}$ ($c$). In SI units Speed of police car is $10$ $\mathrm{m/s}$ ($V_0$). So Doppler effect is described using this equation: $$ f=f_0\left(1+\frac{\Delta V}{c}\right) $$ Where $f_0$ is siren frequency ($f_0=8$ $\mathrm{kHz}$), $c$ is the speed of sound ($c=320$ $\mathrm{m/s}$), and $\Delta V$ is relative speed of observer with source ($\Delta V= 2V_0=20$ $\mathrm{m/s}$). So now lets replace variables with numbers and calculate: $$ f=8\left(1+\frac{20}{320}\right)=8.5\text{ $\mathrm{kHz}$} $$ So Answer is $8.5$ $\mathrm{kHz}$


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