WBJEE · Physics · Waves and Sound
Sound waves are passing through two routes-one in atraight path and the other along a semicireular path of radius \(r\) and are again combined into one pipe and superposed as shown in the figure. If the velocity of sound waves in the pipe is \(v\), then frequencies of resultant waves of maximum amplitude will be integral multiples of 
- A \(\frac{v}{r(\pi-2)}\)
- B \(\frac{v}{r(\pi-1)}\)
- C \(\frac{2 v}{r(\pi-1)}\)
- D \(\frac{v}{r(\pi+1)}\)
Answer & Solution
Correct Answer
(A) \(\frac{v}{r(\pi-2)}\)
Step-by-step Solution
Detailed explanation
Path difference \(=(\pi r-2 r)\) \(=(\pi-2) r=n \lambda\) (wheref \(=\) frequency) \[ \begin{aligned} v &=f \times \lambda \\ \Rightarrow \quad \frac{v}{\lambda} &=f \Rightarrow f=n \left[\frac{v}{(\pi-2) r}\right]^{n} \end{aligned} \] So, multiples integral…
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