question_answer 53)

                  A pipe 20 cm long is closed at one end. Which harmonic mode of the pipe is resonantly existed by a source of 1237.5 Hz? (sound velocity in air \[=330\,\,m\,{{s}^{-1}}\])

Answer:

                  Let nth harmonic be in resonance with the frequency 1237.5Hz.                 In case of a closed ended pipe.                 \[{{v}_{n}}=\,\frac{\upsilon }{4L}\,=\,\frac{4{{v}_{n}}L}{v}\]                 \[=\,\frac{4\times \,1237.5\,\times \,20\,\times \,{{10}^{-2}}\,}{330}\,=\,3\]                 Thus, third harmonic mode of the pipe will be in resonance with a source of frequency 1237.5 Hz.