Question

# An open pipe is suddenly closed at one end. As a result the frequency of third harmonic of the closed pipe is found to be higher by 100 Hz than the fundamental frequency of the open pipe. The fundamental frequency of the open pipe is

A
200 Hz
B
300 Hz
C
240 Hz
D
480 Hz

Solution

## The correct option is B 200 HzFor an organ pipe open at both ends:$$f_n = \dfrac{nv}{2L}$$    .....(1) where $$f$$ stands for for pipe open at both ends$$\Rightarrow$$ Fundamental frequency of the open pipe $$=\dfrac{v}{2L}$$For an organ pipe closed at one end:$$f'_n = \dfrac{(2n-1)v}{4L}$$     .....(2)  where $$f'$$ stands  for pipe closed at One end for third harmonic, $$n=2$$$$f'_3 = \dfrac{3v}{4L}$$Given: $$f'_3 - f_1 = 100$$$$\Rightarrow \dfrac{v}{4L} =100$$$$\Rightarrow f_1 = \dfrac{v}{2L} = 2 \times \dfrac{v}{4L} = 2 \times 100 = 200 \: Hz$$Physics

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