Ncert Exercises & Solutions

A pipe 20 cm long is closed at one end. Which harmonic mode of the pipe is resonantly excited by a source of 1237.5 Hz? (sound velocity in air = 330 ${ms}^{- 1}$ )

Hint: The frequency of the mode will be equal to the frequency of the source.

Step 1 : Find the fundamental frequency of the wave .

Length of pipe, l = 20 cm = 20 \times 10^{- 2} m

v_{fundamental} = \frac{v}{4 L} = \frac{330}{4 \times 20 \times 10^{- 2}} (for closed pipe)

ν_{fundamental} = \frac{330 \times 100}{80} = 412.5 Hz

Step 2 : Find the mode of the pipe .

\frac{ν_{given}}{ν_{fundamental}} = \frac{1237.5}{412.5} = 3

Hence, 3rd harmonic mode of the pipe is resonantly excited by the source of the given frequency.

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