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Process $-1$:An amount of thermal energy $Q$ is added to the material and $\frac{2}{3}$ of the material melts.
Process $-2$:An identical additional amountof thermal energy $Q$ is added to the materlal is now a liquid at $4\,^o C$
........ $^oC$ is the ratio of the latent heat of fusion to the specific heat of the liquid for this material.
[Given: The speed of sound in air is $324 ms ^{-1}$ ]
($1$) When only $S_2$ is emitting sound and it is $Q$, the frequency of sound measured by the detector in $Hz$ is. . . . . .
($2$) Consider both sources emitting sound. When $S_2$ is at $R$ and $S_1$ approaches the detector with a speed $4 ms ^{-1}$, the beat frequency measured by the detector is $\qquad$ $Hz$.

