KCET · Physics · Waves and Sound
A bat flies at a steady speed of \(4 \mathrm{~ms}^{-1}\) emitting a sound of \(\mathrm{f}=90 \times 10^{3} \mathrm{~Hz}\). It is flying horizontally towards a vertical wall. The frequency of the reflected sound as detected by the bat will be (take velocity of sound in air is \(330 \mathrm{~ms}^{-1}\) )
- A \(88.1 \times 10^{3} \mathrm{~Hz}\)
- B \(87.1 \times 10^{3} \mathrm{~Hz}\)
- C \(92.1 \times 10^{3} \mathrm{~Hz}\)
- D \(89.1 \times 10^{3} \mathrm{~Hz}\)
Answer & Solution
Correct Answer
(C) \(92.1 \times 10^{3} \mathrm{~Hz}\)
Step-by-step Solution
Detailed explanation
Frequency of reflected sound heard by the bat
\(v^{\prime} =v\left[\frac{v-\left(v_{0}\right)}{v-v_{s}}\right] \)
\(=v\left[\frac{v+v_{0}}{v-v_{s}}\right]=v\left[\frac{v+v_{b}}{v-v_{b}}\right]\)
\(=v\left[\frac{330+4}{330-4}\right] 90 \times 10^{3} \)
\(=92.1 \times 10^{3} \mathrm{~Hz}\)
\(v^{\prime} =v\left[\frac{v-\left(v_{0}\right)}{v-v_{s}}\right] \)
\(=v\left[\frac{v+v_{0}}{v-v_{s}}\right]=v\left[\frac{v+v_{b}}{v-v_{b}}\right]\)
\(=v\left[\frac{330+4}{330-4}\right] 90 \times 10^{3} \)
\(=92.1 \times 10^{3} \mathrm{~Hz}\)
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