Sound WavesHardBloom L3

Question

In an organ pipe whose one end is at x = 0, the pressure is expressed by p = p0cos $\frac{3\pi x}{2}$sin 300πt where x is in meter and t in sec. The organ pipe can be

Options

A.closed at one end, open at another with length = 0.5m
B.open at both ends, length = 1m
C.closed at both ends, length = 2m
D.closed at one end, open at another with length =$\frac{2}{3}m$

Solution

Sol. K = $\frac{2\pi}{\lambda}$ = $\frac{3\pi}{2}$

⇒ λ = $\frac{4}{3}m$

For pipe closed at both ends

L = $n\frac{\lambda}{2}$

(C) 2 = $n \times \frac{2}{3}$ ⇒ n = 3

For pipe closed at one end

⇒ L = $\left( n + \frac{1}{2} \right)\frac{\lambda}{2}$ No option satisfies for integral value of n

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