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Standard XII

Physics

Resonance

A pipe of 30 ...

Question

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 $m s^{- 1}$ .

Fifth harmonic

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Fourth harmonic

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Third harmonic

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Second harmonic

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Solution

The correct option is D Second harmonic
Given : $ν_{n} = 1.1$ kHz $= 1100$ Hz $v = 330$ $m / s$
Length of pipe $L = 30$ cm $0.3$ m
Frequency of nth harmonic in an open pipe $ν_{n} = \frac{n v}{2 L}$
$∴$ $1100 = \frac{n \times 330}{2 \times 0.3}$ $⟹ n = 2$ i.e. second harmonic

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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 ms−1.

The correct option is D Second harmonicGiven : νn=1.1 kHz =1100 Hz v=330 m/sLength of pipe L=30 cm 0.3 mFrequency of nth harmonic in an open pipe νn=nv2L∴ 1100=n×3302×0.3 ⟹n=2 i.e. second harmonic

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 $m s^{- 1}$ .

The correct option is D Second harmonic
Given : $ν_{n} = 1.1$ kHz $= 1100$ Hz $v = 330$ $m / s$
Length of pipe $L = 30$ cm $0.3$ m
Frequency of nth harmonic in an open pipe $ν_{n} = \frac{n v}{2 L}$
$∴$ $1100 = \frac{n \times 330}{2 \times 0.3}$ $⟹ n = 2$ i.e. second harmonic