A) \[\upsilon /2\]
B) \[\upsilon /\sqrt{2}\]
C) \[\upsilon /4\]
D) \[\upsilon /3\]
Correct Answer: D
Solution :
Let\[f\]be the frequency of horn emitted by car. \[f'=\]observed frequency \[\because \]pitch \[\propto f\] \[\therefore \]\[f'=f+f\] One octave = frequency of instrument \[\therefore \] \[f'=\frac{\upsilon -{{\upsilon }_{O}}}{\upsilon -{{\upsilon }_{S}}}f\] \[{{\upsilon }_{O}}=\]velocity of observer let it be\[u.\] \[{{\upsilon }_{S}}=\]velocity of source because here source and observer (car) both are same and moving with same velocity. \[\therefore \] \[{{\upsilon }_{S}}={{\upsilon }_{O}}=u\] \[\upsilon =\]velocity of sound. \[AB=\]source and sound are in same direction. Hence \[(\upsilon -u)=\]relative velocity. \[BA=\]Observer and sound are in opposite direction hence \[v+u=\]relative velocity \[\therefore \] \[f'=\frac{\upsilon -u}{\upsilon +u}f\] \[2f=\frac{\upsilon -u}{\upsilon +u}f\] \[2\upsilon +2u=\upsilon -u\] \[\upsilon =3u\] \[u=\upsilon /3.\]
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