The pitch of a whistle of an engine appears to drop by $30 \%$ of original value when it passes a stationary…

The pitch of a whistle of an engine appears to drop by $30 \%$ of original value when it passes a stationary observer. If the speed of sound in air is $350 \mathrm{~ms}^{-1}$, then the speed of engine in $\mathrm{ms}^{-1}$ is
  1. 840
  2. 700
  3. 175
  4. 150

Solution

Speed of sound $=350 \mathrm{~m} / \mathrm{s}$ Also,' ....(given) $\mathrm{n}^{\prime}=\mathrm{n}-\frac{30}{100} \mathrm{n}=\frac{70}{100} \mathrm{n}=0.7 \mathrm{n}$
If $n$ is the original (actual) frequency of the whistle and $\mathrm{n}^{\prime}$ the frequency as the engine passes the stationary observer, then $\begin{array}{ll} & \frac{\mathrm{n}^{\prime}}{\mathrm{n}}=\left(\frac{\mathrm{v}}{\mathrm{v}+\mathrm{v}_{\text {cngine }}}\right) \\ \therefore \quad & 0.7=\frac{350}{350+\mathrm{v}_{\text {engine }}} \\ & 0.7 \mathrm{y}_{\text {engine }}+245=350 \\ \therefore \quad & \mathrm{v}_{\text {engine }}=150 \mathrm{~m} / \mathrm{s}\end{array}$

Asked in: MHT CET 2024 (03 May Shift 1)

Practice more Waves and Sound questions on Aicharya