When an open pipe is closed from one end, the | vedclass

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(A) Let the length of the pipe be $\ell$ and the speed of sound be $v$.For an open pipe, the fundamental frequency is $f_0 = \frac{v}{2\ell}$. The $2^

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$300$

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(A) Let the length of the pipe be $\ell$ and the speed of sound be $v$.For an open pipe, the fundamental frequency is $f_0 = \frac{v}{2\ell}$. The $2^{nd}$ overtone of an open pipe is $3f_0 = \frac{3v}{2\ell}$.For a closed pipe, the fundamental frequency is $f_c = \frac{v}{4\ell}$. The $3^{rd}$ overtone of a closed pipe is $7f_c = \frac{7v}{4\ell}$.According to the problem, the $3^{rd}$ overtone of the closed pipe is $150 \,Hz$ higher than the $2^{nd}$ overtone of the open pipe:$\frac{7v}{4\ell} = \frac{3v}{2\ell} + 150$$\frac{7v}{4\ell} - \frac{6v}{4\ell} = 150$$\frac{v}{4\ell} = 150$Since the fundamental frequency of the open pipe is $f_0 = \frac{v}{2\ell}$, we can write:$f_0 = 2 	imes \left(\frac{v}{4\ell}ight) = 2 	imes 150 = 300 \,Hz$.

When an open pipe is closed from one end, the third overtone of the closed pipe is higher in frequency by $150 \,Hz$ than the second overtone of the open pipe. The fundamental frequency of the open pipe will be: (in $\,Hz$)

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