Question

A pipe 30cm long, is open at both ends. Which harmonic mode of the pipe resonates a 1.1kHz sources? The speed of sound in air is 330m/s​

Answer 1

Answer :-

Given,

• Speed of sound (v) = 330 m/s
• Length of pipe (L) = 30 cm

Since the pipe is open at both ends, the frequency of its nth harmonic will be $vn = \frac{nv}{2</strong><strong>L</strong><strong>}$ where n = 1, 2, 3....... and $n = \frac{2</strong><strong>L</strong><strong>vn}{v}$

Let nth harmonic of open pipe resonate with 1.1 kHz source i.e.,

$vn = 1.1 \: k</strong><strong>H</strong><strong>z = 1.1 \times {10}^{3} </strong><strong>H</strong><strong>z$

Hence,

$n = \frac{2 \times 30 \times {10}^{ - 2} \times 1.1 \times {10}^{ - 3} }{330} \\ n = 2$

•°• The second harmonic mode of the pipe resonates a 1.1 kHz source.

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