Wave and Acoustics | Physics JEE previous year questions with Solutions

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Topic Question Set

Q 11 :

A guitar string of length 90 cm vibrates with a fundamental frequency of 120 Hz. The length of the string producing a fundamental frequency of 180 Hz will be ______ cm. [2023]

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(60)

$f = \frac{m v}{2 l}, for fundamental mode n = 1$

$f = \frac{v}{2 l} \Rightarrow f \propto \frac{1}{l}$

$\frac{f_{1}}{f_{2}} \propto \frac{l_{2}}{l_{1}}$

$\Rightarrow \frac{120}{180} = \frac{l_{2}}{90} \Rightarrow l_{2} = 60 cm$

Q 12 :

A wire of density $8 \times 10^{3} {kg/m}^{3}$ is stretched between two clamps 0.5 m apart. The extension developed in the wire is $3.2 \times 10^{- 4} m$ . If $Y = 8 \times 10^{10} {N/m}^{2}$ , the fundamental frequency of vibration in the wire will be ________ Hz. [2023]

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(80)

$f = \frac{1}{2 L} \sqrt{\frac{T}{μ}} = \frac{1}{2 L} \sqrt{\frac{Y A Δ L}{ρ A L}}$

$f = 80 Hz$

Q 13 :

For a certain organ pipe, the first three resonance frequencies are in the ratio of 1 : 3 : 5 respectively. If the frequency of fifth harmonic is 405 Hz and the speed of sound in air is 324 ${ms}^{- 1}$ , the length of the organ pipe is ______ m. [2023]

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(1)

For 5th harmonic in a closed organ pipe,

$f_{5} = \frac{5 v}{4 ℓ}$

$\Rightarrow 405 = \frac{5 \times 324}{4 ℓ}$

$\Rightarrow ℓ = 1 m$

Q 14 :

In an experiment with sonometer, when a mass of 180 g is attached to the string, it vibrates with fundamental frequency of 30 Hz. When a mass m is attached, the string vibrates with fundamental frequency of 50 Hz. The value of m is ______ g. [2023]

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(500)

$f = \frac{1}{2 ℓ} \sqrt{\frac{T}{μ}} (T : Tension)$

$\frac{f_{2}}{f_{1}} = \sqrt{\frac{T_{2}}{T_{1}}}$

${(\frac{50}{30})}^{2} = \frac{m g}{180 g}$ $\Rightarrow m = \frac{25}{9} \times 180 = 500 gram$

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