A source $(S)$ of sound has frequency $240 \ Hz$. When the observer $(O)$ and the source move towards each other at a speed $v$ with respect to the ground (as shown in Case $1$ in the figure), the observer measures the frequency of the sound to be $288 \ Hz$. However, when the observer and the source move away from each other at the same speed $v$ with respect to the ground (as shown in Case $2$ in the figure), the observer measures the frequency of sound to be $n Hz$. The value of $n$ is. . . . . .
IIT 2024, Advanced
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Frequency received by observer $f_0=\left(\frac{C \pm V_0}{C \pm V_s}\right) f_s, C$ is speed of sound
Case-$1$:
$f _1=\left(\frac{ C + V }{ C - V }\right) f _{ s }$
$288=\left(\frac{ C + V }{ C - V }\right) 240$
Case-$2$:
$f _2=\left(\frac{ C - V }{ C + V }\right) f _{ s }$
$n =\left(\frac{ C - V }{ C + V }\right) 2400$
multiply the two equations, we get.
$(288)( n )=(240)(240)$
$N =200$
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