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  • A pipe of 30 cm long and open at both the ends produces harmonics. Which harmonic mode of pipe resonates a 1.1 kHz source? (Given, speed of sound in air = 330 m/s<strong

A pipe of 30 cm long and open at both the ends produces harmonics. Which harmonic mode of pipe resonates a 1.1 kHz source? (Given, speed of sound in air = 330 m/s

Option: 1

Fifth harmonic


Option: 2

Fourth harmonic


Option: 3

Third harmonic


Option: 4

Second harmonic


Answers (1)

best_answer

First mode of Vibration v_{1\,} = \frac{V}{2l} -\: \left ( 1 \right ) 

The frequency of nth mode of vibration-

V_n=n \times v_1=n \times\left(\frac{V}{2 l}\right)

Given, V_n=1.5 \mathrm{kHz}=1100 \mathrm{~Hz} \Rightarrow te =330 \mathrm{~m} / \mathrm{s} \:\\\\ and\: l=30 \mathrm{~cm}=0.30 \mathrm{~m}\\\\ \begin{aligned} & 1100=n \times\left(\frac{330}{2 \times 0.30}\right) \\ & n=\frac{1100 \times 2 \times 0.30}{330} \\ & n=\frac{660}{330}=2 \end{aligned}

So, second harmonic mode of pipe resontes.

Posted by

shivangi.shekhar

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