Wave and Acoustics | Physics JEE previous year questions with Solutions

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

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

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

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

Q 5 :
The fundamental frequency of a closed organ pipe is equal to the first overtone frequency of an open organ pipe. If the length of the open pipe is 60 cm, the length of the closed pipe will be [2024]

30 cm
45 cm
60 cm
15 cm

1

2

3

4

(4)

$\frac{λ}{4} = L_{1}$ $2 (\frac{λ}{2}) = λ = L_{2}$

$f_{1} = \frac{v}{4 L_{1}}$ $f_{2} = \frac{v}{L_{2}}$

$f_{1} = f_{2}$

$\frac{v}{4 L_{1}} = \frac{v}{L_{2}} \Rightarrow L_{2} = 4 L_{1}$

$60 = 4 \times L_{1} \Rightarrow L_{1} = 15 cm$

Q 6 :
A sonometer wire of resonating length 90 cm has a fundamental frequency of 400 Hz when kept under some tension. The resonating length of the wire with a fundamental frequency of 600 Hz under the same tension is ____ cm. [2024]

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(60)

$f_{0} = 400 Hz; v = \sqrt{\frac{T}{μ}} = constant$

$\frac{λ}{2} = L; v = f_{0} λ$

$\frac{v}{2 f_{0}} = L \Rightarrow v = 2 L f_{0}$

$L' = \frac{v}{2 f'} = \frac{2 L f_{0}}{2 f'}$

$= \frac{L f_{0}}{f'} = \frac{90 \times 400}{600} = 60$

Q 7 :
Two open organ pipes of lengths 60 cm and 90 cm resonate at 6th and 5th harmonics respectively. The difference of frequencies for the given modes is ____ Hz

(Velocity of sound in air = 333 m/s) [2024]

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(740)

For first open organ pipe

$f = \frac{n v}{2 l} \Rightarrow f_{6} = \frac{6 v}{2 l_{1}}$

$f_{6} = \frac{6 v}{2 (0.6)} = 5 v$ ...(i)

For second open organ pipe

$f_{5} = \frac{5 v}{2 (l_{2})} = \frac{5 v}{2 (0.9)} = \frac{25}{9} v$ ...(ii)

$Δ f = f_{6} - f_{5} = 5 v - \frac{25 v}{9}$

$Δ f = \frac{(45 - 25) v}{9} = \frac{20}{9} v = \frac{20}{9} \times 333 \Rightarrow Δ f = 740 Hz$

Q 8 :
A closed organ and an open organ tube filled by two different gases having same bulk modulus but different densities $ρ_{1}$ and $ρ_{2}$ respectively. The frequency of 9th harmonic of closed tube is identical with 4th harmonic of open tube. If the length of the closed tube is 10 cm and the density ratio of the gases is $ρ_{1} : ρ_{2} = 1 : 16$ , then the length of the open tube is [2025]

$\frac{20}{7} cm$
$\frac{15}{7} cm$
$\frac{20}{9} cm$
$\frac{15}{9} cm$

1

2

3

4

(3)

9th harmonic of closed pipe = $\frac{9 v_{1}}{4 l_{1}}$

4th harmonic of open pipe = $\frac{2 v_{2}}{l_{1}}$

$∴ \frac{9 v_{1}}{4 l_{1}} = \frac{2 v_{2}}{l_{1}}$

$∴ \frac{9}{4 l_{1}} \sqrt{\frac{B}{ρ_{1}}} = \frac{2}{l_{2}} \sqrt{\frac{B}{ρ_{2}}}$

$\Rightarrow \frac{l_{2}}{l_{1}} = \frac{8}{9} \sqrt{\frac{ρ_{1}}{ρ_{2}}}$

$l_{2} = l_{1} \times \frac{8}{9} \times \frac{1}{4} = \frac{20}{9} cm$

Q 9 :
In an experiment with a closed organ pipe, it is filled with water by $(\frac{1}{5}) th$ of its volume. The frequency of the fundamental note will change by [2025]

25%
20%
–20%
–25%

1

2

3

4

(1)

$f_{1} = \frac{v}{2}, f_{2} = \frac{v}{2 (\frac{4 l}{5})} = \frac{5}{4} f_{1} = 1.25 f_{1}$

$100 \times \frac{△ f}{f} = 25 %$

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]

0%

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]

0%

0%

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]

0%

Q 5 :
The fundamental frequency of a closed organ pipe is equal to the first overtone frequency of an open organ pipe. If the length of the open pipe is 60 cm, the length of the closed pipe will be [2024]

Q 6 :
A sonometer wire of resonating length 90 cm has a fundamental frequency of 400 Hz when kept under some tension. The resonating length of the wire with a fundamental frequency of 600 Hz under the same tension is ____ cm. [2024]

0%

Q 7 :
Two open organ pipes of lengths 60 cm and 90 cm resonate at 6th and 5th harmonics respectively. The difference of frequencies for the given modes is ____ Hz

(Velocity of sound in air = 333 m/s) [2024]

0%

Q 9 :
In an experiment with a closed organ pipe, it is filled with water by $(\frac{1}{5}) th$ of its volume. The frequency of the fundamental note will change by [2025]

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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 (a-1a) then the value of a is _________ . [2024]

0%

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]

0%

0%

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]

0%

Q 5 : The fundamental frequency of a closed organ pipe is equal to the first overtone frequency of an open organ pipe. If the length of the open pipe is 60 cm, the length of the closed pipe will be [2024]

Q 6 : A sonometer wire of resonating length 90 cm has a fundamental frequency of 400 Hz when kept under some tension. The resonating length of the wire with a fundamental frequency of 600 Hz under the same tension is ____ cm. [2024]

0%

Q 7 : Two open organ pipes of lengths 60 cm and 90 cm resonate at 6th and 5th harmonics respectively. The difference of frequencies for the given modes is ____ Hz (Velocity of sound in air = 333 m/s) [2024]

0%

Q 9 : In an experiment with a closed organ pipe, it is filled with water by (15)th of its volume. The frequency of the fundamental note will change by [2025]

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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]

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]

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]

Q 5 :
The fundamental frequency of a closed organ pipe is equal to the first overtone frequency of an open organ pipe. If the length of the open pipe is 60 cm, the length of the closed pipe will be [2024]

Q 6 :
A sonometer wire of resonating length 90 cm has a fundamental frequency of 400 Hz when kept under some tension. The resonating length of the wire with a fundamental frequency of 600 Hz under the same tension is ____ cm. [2024]

Q 7 :
Two open organ pipes of lengths 60 cm and 90 cm resonate at 6th and 5th harmonics respectively. The difference of frequencies for the given modes is ____ Hz

(Velocity of sound in air = 333 m/s) [2024]

Q 9 :
In an experiment with a closed organ pipe, it is filled with water by $(\frac{1}{5}) th$ of its volume. The frequency of the fundamental note will change by [2025]