Wave and Acoustics | Physics JEE previous year questions with Solutions

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Topic Question Set

Q 1 :
A closed and an open organ pipe have same lengths. If the ratio of frequencies of their seventh overtones is $(\frac{a - 1}{a})$ then the value of $a$ is _________ . [2024]

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(16) For closed organ pipe

$f_{c} = (2 n + 1) \frac{v}{4 l} = \frac{15 v}{4 l}$

For open organ pipe

$f_{o} = (n + 1) \frac{v}{2 l} = \frac{8 v}{2 l}$

$\frac{f_{c}}{f_{o}} = \frac{15}{16} = \frac{a - 1}{a} \Rightarrow a = 16$

Q 2 :
A closed organ pipe 150 cm long gives 7 beats per second with an open organ pipe of length 350 cm, both vibrating in fundamental mode. The velocity of sound is _______ m/s. [2024]

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(294) $f_{c} = \frac{v}{4 l_{1}}$ $f_{o} = \frac{v}{2 l_{2}}$

$\frac{v}{4 \times 150} - \frac{v}{2 \times 350} = 7$

$\frac{v}{600 c m} - \frac{v}{700 c m} = 7$

$\frac{v}{6 m} - \frac{v}{7 m} = 7$

$v (\frac{1}{42}) = 7$

$v = 42 \times 7 = 294 m / s$

Q 3 :
In a closed organ pipe, the frequency of fundamental note is 30 Hz. A certain amount of water is now poured in the organ pipe so that the fundamental frequency is increased to 110 Hz. If the organ pipe has a cross-sectional area of $2$ $c m^{2}$ , the amount of water poured in the organ tube is ________ g. (Take speed of sound in air is 330 m/s) [2024]

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(400)

Q 4 :
A tuning fork resonates with a sonometer wire of length 1 m stretched with a tension of 6 N. When the tension in the wire is changed to 54 N, the same tuning fork produces 12 beats per second with it. The frequency of the tuning fork is ________ Hz. [2024]

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(6) $f = \frac{1}{2 L} \sqrt{\frac{T}{μ}}$

$f_{1} = \frac{1}{2} \sqrt{\frac{6}{μ}},$ $f_{2} = \frac{1}{2} \sqrt{\frac{54}{μ}}$

$\frac{f_{1}}{f_{2}} = \frac{1}{3},$ $f_{2} - f_{1} = 12$

$f_{1} = 6$ $H z$

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