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]

(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]

(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]

(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]

(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]

(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]

(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 = $\frac{2 v_{2}}{l_{2}}$

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

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

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

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

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)

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

$100 \times \frac{△ f}{f} = 25 %$

Q 10 :

An organ pipe 40 cm long is open at both ends. The speed of sound in air is 360 ${ms}^{- 1}$ . The frequency of the second harmonic is ______ Hz. [2023]

(900)

For second harmonic of an open organ pipe, $L = λ$

So the frequency of vibration is $f = \frac{v}{λ}$

$f = \frac{V}{λ} = \frac{V}{L} = \frac{360}{\frac{40}{100}} = 900 Hz$

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]

(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]

(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]

(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]

(500)

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

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

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

Q 15 :

The fifth harmonic of a closed organ pipe is found to be in unison with the first harmonic of an open pipe. The ratio of lengths of closed pipe to that of the open pipe is $\frac{5}{x}$ . The value of $x$ is _______ . [2026]

1
3
4
2

1

2

3

4

(4)

$f_{5 closed} = f_{1 open}$

$\frac{5 v}{4 L_{closed}} = \frac{v}{2 L_{open}}$

$\frac{L_{closed}}{L_{open}} = \frac{5}{2}$

$x = 2$

Q 16 :

In an open organ pipe $v_{3}$ and $v_{6}$ are 3rd and 6th harmonic frequencies, respectively. If $v_{6} - v_{3} = 2200 Hz,$ the length of the pipe is _______ mm.

(Take velocity of sound in air is 330 m/s) [2026]

200
250
275
225

1

2

3

4

(4)

$f = n (\frac{V_{0}}{2 L})$

$\frac{6 V_{0}}{2 L} - \frac{3 V_{0}}{2 L} = 2200$

$\frac{3 V_{0}}{2 L} = 2200$

$\frac{3 \times 330}{2 \times L} = 2200$

$L = \frac{3 \times 330}{2 \times 2200}$

$L = 0.225 m$

$L = 225 mm$

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]

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]

Q 10 :

An organ pipe 40 cm long is open at both ends. The speed of sound in air is 360 ${ms}^{- 1}$ . The frequency of the second harmonic is ______ Hz. [2023]

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]

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]

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]

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]

Q 15 :

The fifth harmonic of a closed organ pipe is found to be in unison with the first harmonic of an open pipe. The ratio of lengths of closed pipe to that of the open pipe is $\frac{5}{x}$ . The value of $x$ is _______ . [2026]

Q 16 :

In an open organ pipe $v_{3}$ and $v_{6}$ are 3rd and 6th harmonic frequencies, respectively. If $v_{6} - v_{3} = 2200 Hz,$ the length of the pipe is _______ mm.

(Take velocity of sound in air is 330 m/s) [2026]

Want Us to Email you About Special Offers & Updates?

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]

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 (15)th of its volume. The frequency of the fundamental note will change by [2025]

Q 10 : An organ pipe 40 cm long is open at both ends. The speed of sound in air is 360 ms-1. The frequency of the second harmonic is ______ Hz. [2023]

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]

Q 12 : A wire of density 8×103 kg/m3 is stretched between two clamps 0.5 m apart. The extension developed in the wire is 3.2×10-4 m. If Y=8×1010 N/m2, the fundamental frequency of vibration in the wire will be ________ Hz. [2023]

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]

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]

Q 15 : The fifth harmonic of a closed organ pipe is found to be in unison with the first harmonic of an open pipe. The ratio of lengths of closed pipe to that of the open pipe is 5x. The value of x is _______ . [2026]

Q 16 : In an open organ pipe v3 and v6 are 3rd and 6th harmonic frequencies, respectively. If v6-v3=2200 Hz, the length of the pipe is _______ mm. (Take velocity of sound in air is 330 m/s) [2026]

Want Us to Email you About Special Offers & Updates?

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]

Q 10 :

An organ pipe 40 cm long is open at both ends. The speed of sound in air is 360 ${ms}^{- 1}$ . The frequency of the second harmonic is ______ Hz. [2023]

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]

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]

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]

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]

Q 15 :

The fifth harmonic of a closed organ pipe is found to be in unison with the first harmonic of an open pipe. The ratio of lengths of closed pipe to that of the open pipe is $\frac{5}{x}$ . The value of $x$ is _______ . [2026]

Q 16 :

In an open organ pipe $v_{3}$ and $v_{6}$ are 3rd and 6th harmonic frequencies, respectively. If $v_{6} - v_{3} = 2200 Hz,$ the length of the pipe is _______ mm.

(Take velocity of sound in air is 330 m/s) [2026]