Wave and Acoustics | Physics JEE previous year questions with Solutions

Q 1 :
Two waves of intensity ratio 1:9 cross each other at a point. The resultant intensities at that point, when

(a) Waves are in coherent is $I_{1}$

(b) Waves are coherent is $I_{2}$ and differ in phase by 60. If $\frac{I_{1}}{I_{2}} = \frac{10}{x}$ then $x =$ ___________ . [2024]

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(13) For incoherent wave $I_{1} = I_{A} + I_{B} \Rightarrow I_{1} = I_{0} + 9 I_{0}$

$I_{1} = 10 I_{0}$

For coherent wave $I_{2} = I_{A} + I_{B} + 2 \sqrt{I_{A} I_{B}} \cos 60^{0}$

$I_{2} = I_{0} + 9 I_{0} + 2 \sqrt{9 I_{0}^{2}} \cdot \frac{1}{2} = 13 I_{0}$

$\frac{I_{1}}{I_{2}} = \frac{10}{13}$

Q 2 :
In the resonance experiment, two air columns (closed at one end) of 100 cm and 120 cm long, give 15 beats per second when each one is sounding in the respective fundamental modes. The velocity of sound in the air column is: [2025]

335 m/s
370 m/s
340 m/s
360 m/s

1

2

3

4

(4)

Fundamental frequency in close organ pipe, $f_{0} = \frac{v}{4 l}$ , $f_{1} = \frac{v}{4 l_{1}}$ and $f_{2} = \frac{v}{4 l_{2}}$

Beat $△ f = (f_{1} - f_{2}) = \frac{v}{4} (\frac{1}{l_{1}} - \frac{1}{l_{2}})$

$15 = \frac{v}{4} (\frac{1}{1} - \frac{1}{1.2})$

$\Rightarrow v = 360 m / s$

Q 3 :
Two harmonic waves moving in the same direction superimpose to form a wave x = a cos (1.5t) cos (50.5t) where t is in seconds. Find the period with which they beat (close to nearest integer) [2025]

6 s
4 s
1 s
2 s

1

2

3

4

(4)

The given equation can be written as

$x = \frac{a}{2} \cos [1.5 + 50.5] t + \frac{a}{2} \cos [50.5 - 1.5] t$

$x = \frac{a}{2} \cos [52 t] + \frac{a}{2} \cos [49 t]$

Here, $2 π f_{1} = 52 and 2 π f_{2} = 49$

$f_{1} = \frac{52}{2 π}, f_{2} = \frac{49}{2 π}$

$\Rightarrow △ f = f_{Beat} = f_{1} - f_{2} = \frac{3}{2 π} Hz$

$∴ T_{Beat} = \frac{1}{f_{Beat}} \frac{2 π}{3} \sec = 2.09 \sec$

$\Rightarrow T_{Beat} = 2 \sec$

Q 4 :
The amplitude and phase of a wave that is formed by the superposition of two harmonic travelling waves, $y_{1} (x, t) = 4 \sin (k x - ω t)$ and $y_{2} (x, t) = 2 \sin (k x - ω t + \frac{2 π}{3})$ , are: (Take the angular frequency of initial waves same as $ω$ ) [2025]

$[6, \frac{2 π}{3}]$
$[6, \frac{π}{3}]$
$[\sqrt{3}, \frac{π}{6}]$
$[2 \sqrt{3}, \frac{π}{6}]$

1

2

3

4

(4)

$A = \sqrt{A_{1}^{2} + A_{2}^{2} + 2 A_{1} A_{2} \cos ϕ}$

Here, $ϕ = \frac{2 π}{3}$

$A = \sqrt{4^{2} + 2^{2} + 2 \times 4 \times 2 \cos \frac{2 π}{3}} = 2 \sqrt{3}$

$\tan α = \frac{2 \sin ϕ}{4 + 2 \cos ϕ} = \frac{1}{\sqrt{3}} \Rightarrow α = π / 6$

Topic Question Set

Q 1 :
Two waves of intensity ratio 1:9 cross each other at a point. The resultant intensities at that point, when

(a) Waves are in coherent is $I_{1}$

(b) Waves are coherent is $I_{2}$ and differ in phase by 60. If $\frac{I_{1}}{I_{2}} = \frac{10}{x}$ then $x =$ ___________ . [2024]

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Q 2 :
In the resonance experiment, two air columns (closed at one end) of 100 cm and 120 cm long, give 15 beats per second when each one is sounding in the respective fundamental modes. The velocity of sound in the air column is: [2025]

Q 3 :
Two harmonic waves moving in the same direction superimpose to form a wave x = a cos (1.5t) cos (50.5t) where t is in seconds. Find the period with which they beat (close to nearest integer) [2025]

Q 4 :
The amplitude and phase of a wave that is formed by the superposition of two harmonic travelling waves, $y_{1} (x, t) = 4 \sin (k x - ω t)$ and $y_{2} (x, t) = 2 \sin (k x - ω t + \frac{2 π}{3})$ , are: (Take the angular frequency of initial waves same as $ω$ ) [2025]

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Topic Question Set

Q 1 : Two waves of intensity ratio 1:9 cross each other at a point. The resultant intensities at that point, when (a) Waves are in coherent is I1 (b) Waves are coherent is I2 and differ in phase by 60. If I1I2=10x then x= ___________ . [2024]

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Q 2 : In the resonance experiment, two air columns (closed at one end) of 100 cm and 120 cm long, give 15 beats per second when each one is sounding in the respective fundamental modes. The velocity of sound in the air column is: [2025]

Q 3 : Two harmonic waves moving in the same direction superimpose to form a wave x = a cos (1.5t) cos (50.5t) where t is in seconds. Find the period with which they beat (close to nearest integer) [2025]

Q 4 : The amplitude and phase of a wave that is formed by the superposition of two harmonic travelling waves, y1(x,t)=4 sin (kx–ωt) and y2(x,t)=2 sin (kx–ωt+2π3), are: (Take the angular frequency of initial waves same as ω) [2025]

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Q 1 :
Two waves of intensity ratio 1:9 cross each other at a point. The resultant intensities at that point, when

(a) Waves are in coherent is $I_{1}$

(b) Waves are coherent is $I_{2}$ and differ in phase by 60. If $\frac{I_{1}}{I_{2}} = \frac{10}{x}$ then $x =$ ___________ . [2024]

Q 2 :
In the resonance experiment, two air columns (closed at one end) of 100 cm and 120 cm long, give 15 beats per second when each one is sounding in the respective fundamental modes. The velocity of sound in the air column is: [2025]

Q 3 :
Two harmonic waves moving in the same direction superimpose to form a wave x = a cos (1.5t) cos (50.5t) where t is in seconds. Find the period with which they beat (close to nearest integer) [2025]

Q 4 :
The amplitude and phase of a wave that is formed by the superposition of two harmonic travelling waves, $y_{1} (x, t) = 4 \sin (k x - ω t)$ and $y_{2} (x, t) = 2 \sin (k x - ω t + \frac{2 π}{3})$ , are: (Take the angular frequency of initial waves same as $ω$ ) [2025]