A pipe 20 mathrm{cm} long is closed at one end. Which harmonic mode of pipe is resonantly exci

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14.Waves and Sound

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A pipe $20$ $\mathrm{cm}$ long is closed at one end. Which harmonic mode of the pipe is resonantly excited by a source of $1237.5$ $\mathrm{Hz}$ ?( sound velocity in air $= 330$ $\mathrm{m/s}$ ).

Option A

Option B

Option C

Option D

Solution

Here $f=1237.5 \mathrm{~Hz}$

$f_{1}=\frac{v}{4 \mathrm{~L}}=\frac{330}{4 \times 0.2}=412.5 \mathrm{~Hz}$

Now, $\frac{f}{f_{1}}=\frac{1237.5}{412.5}=3$

Air column in closed pipe will resonate in second mode of vibration with third harmonic. $\left(\because f=3 f_{1}\right)$

Standard 11

Physics

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