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Mechanical Properties Of Fluids

Question
CBSEENPH11020660

A source of sound S emitting waves of frequency 100 Hz and an observer O are located at some distance from each other. The source is moving with a speed of 19.4 ms-1 at an angle of 60o with the source observer is at rest. the apparent frequency observed by the observer (velocity of sound in air 330 ms-1) is 

  • 100 Hz

  • 103 Hz

  • 106 Hz

  • 97 Hz

Solution

B.

103 Hz

Given, as a source of sound S emitting waves of frequency 100 Hz and an observer O are located at some distance. Such that, source is moving with a speed of 19.4 m/s  at angle 60o with source- observer line as shown in figure

The apparent frequency heard by observer
straight f subscript straight o space equals space straight f subscript straight s open square brackets fraction numerator straight V over denominator straight v minus straight v subscript straight s space cos space 60 to the power of straight o end fraction close square brackets space equals space 100 space open square brackets fraction numerator 330 over denominator 330 minus 19.4 space straight x begin display style 1 half end style end fraction close square brackets

equals space 100 space open square brackets fraction numerator 330 over denominator 300 minus 9.7 end fraction close square brackets space equals space 100 open square brackets fraction numerator 330 over denominator 320.3 end fraction close square brackets

equals space 103.02 space Hz