Wave and Acoustics | Physics JEE previous year questions with Solutions

Q 1 :
A plane progressive wave is given by $y = 2$ $\cos$ $2 π (330 t - x) m .$ The frequency of the wave is [2024]

340 Hz
165 Hz
330 Hz
660 Hz

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(3)

$y = 2$ $\cos$ $2 π (330 t - x) m$

$y = A$ $\cos$ $(ω t - k x)$

Comparing $ω = 2 π \times 330$

$2 πf = 2 π \times 330 \Rightarrow f = 330$ $H z$

Q 2 :
The equation of a transverse wave travelling along a string is $y (x, t) = 4.0 \sin [20 \times 10^{- 3} x + 600 t] mm$ , where x is in the mm and t is in second. The velocity of the wave is [2025]

+ 30 m/s
– 60 m/s
– 30 m/s
+ 60 m/s

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4

(3)

$y = 4 \sin [(20 \times 10^{- 3} x + 600 t)$

Here, $ω$ = 600 and k = $20 \times 10^{- 3}$

$∴ v = \frac{ω}{k} = \frac{600}{20 \times 10^{- 3}}$

$= 30 \times 10^{+ 3} mm / s = 30 m / s$

abd direction is towards –ve x-axis

$∴$ v = – 30 m/s

Q 3 :
A sinusoidal wave of wavelength 7.5 cm travels a distance of 1.2 cm along the x-direction in 0.3 sec. The crest P is at x = 0 at t = 0 sec and maximum displacement of the wave is 2 cm. With equation correctly represents this wave? [2025]

y = 2 cos (0.83x – 3.35t) cm
y = 2 sin (0.83x – 3.35t) cm
y = 2 cos (3.35x – 0.83t) cm
y = 2 cos (0.13x – 0.5t) cm

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(1)

$v = \frac{distance}{time}$

$v = \frac{1.2}{0.3} = 4 cm / s$

$k = \frac{2 π}{λ} = \frac{2 π}{7.5} = \frac{4 π}{15} = 0.83$

$v = \frac{ω}{k} \Rightarrow ω = v k = 4 \times \frac{4 π}{15} = 3.35$

At t = 0, x = 0, there is a crest

So, y = A cos (kx – $ω$ t)

$∴$ y = 2 cos (0.83x – 3.35t) cm

Q 4 :
Displacement of a wave is expressed as $x (t) = 5 \cos (628 t + \frac{π}{2}) m$ . The wavelength of the wave when its velocity is 300 m/s is [2025]

5 m
3 m
0.5 m
0.33 m

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(2)

$x (t) = 5 \cos [628 t + \frac{π}{2}] m$

Wave velocity v = 300 m/s

$v = \frac{ω}{k}$

$300 = \frac{628}{K} \Rightarrow K = \frac{628}{300} m^{- 1}$

$\frac{2 π}{λ} = \frac{628}{300} \Rightarrow λ = \frac{2 \times 3.14 \times 300}{628}$

$\Rightarrow λ = 3 m$

Q 5 :
The equation of a wave travelling on a string is y = sin [20 $π$ x + 10 $π$ t], where x and t are distance and time in SI units. The minimum distance between two points having the same oscillating speed is : [2025]

0.5 cm
20 cm
10 cm
2.5 cm

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(1)

$k = 20 π = \frac{2 π}{λ} \Rightarrow λ = 10 cm$

Minimum distance between 2 points having same speed is $\frac{λ}{2}$ .

Minimum distance $= \frac{λ}{2} = 5 cm$

Q 6 :
Two strings with circular cross section and made of same material, are stretched to have same amount of tension. A transverse wave is then made to pass through both the strings. The velocity of the wave in the first string having the radius of cross section R is $v_{1}$ , and that in the other string having radius of cross section R/2 is $v_{2}$ . Then $\frac{v_{2}}{v_{1}} =$ [2025]

$\sqrt{2}$
2
8
4

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(2)

$v = \sqrt{\frac{T}{μ}} = \sqrt{\frac{T}{ρ π R^{2}}}$

$\Rightarrow \frac{v_{2}}{v_{1}} = \frac{R_{1}}{R_{2}} = 2$

Topic Question Set

Q 1 :
A plane progressive wave is given by $y = 2$ $\cos$ $2 π (330 t - x) m .$ The frequency of the wave is [2024]

Q 2 :
The equation of a transverse wave travelling along a string is $y (x, t) = 4.0 \sin [20 \times 10^{- 3} x + 600 t] mm$ , where x is in the mm and t is in second. The velocity of the wave is [2025]

Q 3 :
A sinusoidal wave of wavelength 7.5 cm travels a distance of 1.2 cm along the x-direction in 0.3 sec. The crest P is at x = 0 at t = 0 sec and maximum displacement of the wave is 2 cm. With equation correctly represents this wave? [2025]

Q 4 :
Displacement of a wave is expressed as $x (t) = 5 \cos (628 t + \frac{π}{2}) m$ . The wavelength of the wave when its velocity is 300 m/s is [2025]

Q 5 :
The equation of a wave travelling on a string is y = sin [20 $π$ x + 10 $π$ t], where x and t are distance and time in SI units. The minimum distance between two points having the same oscillating speed is : [2025]

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Topic Question Set

Q 1 : A plane progressive wave is given by y=2 cos 2π(330t-x)m. The frequency of the wave is [2024]

Q 2 : The equation of a transverse wave travelling along a string is y(x,t)=4.0 sin [20×10–3x+600 t] mm, where x is in the mm and t is in second. The velocity of the wave is [2025]

Q 3 : A sinusoidal wave of wavelength 7.5 cm travels a distance of 1.2 cm along the x-direction in 0.3 sec. The crest P is at x = 0 at t = 0 sec and maximum displacement of the wave is 2 cm. With equation correctly represents this wave? [2025]

Q 4 : Displacement of a wave is expressed as x(t)=5 cos (628t+π2) m. The wavelength of the wave when its velocity is 300 m/s is [2025]

Q 5 : The equation of a wave travelling on a string is y = sin [20 πx + 10 πt], where x and t are distance and time in SI units. The minimum distance between two points having the same oscillating speed is : [2025]

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Q 1 :
A plane progressive wave is given by $y = 2$ $\cos$ $2 π (330 t - x) m .$ The frequency of the wave is [2024]

Q 2 :
The equation of a transverse wave travelling along a string is $y (x, t) = 4.0 \sin [20 \times 10^{- 3} x + 600 t] mm$ , where x is in the mm and t is in second. The velocity of the wave is [2025]

Q 3 :
A sinusoidal wave of wavelength 7.5 cm travels a distance of 1.2 cm along the x-direction in 0.3 sec. The crest P is at x = 0 at t = 0 sec and maximum displacement of the wave is 2 cm. With equation correctly represents this wave? [2025]

Q 4 :
Displacement of a wave is expressed as $x (t) = 5 \cos (628 t + \frac{π}{2}) m$ . The wavelength of the wave when its velocity is 300 m/s is [2025]

Q 5 :
The equation of a wave travelling on a string is y = sin [20 $π$ x + 10 $π$ t], where x and t are distance and time in SI units. The minimum distance between two points having the same oscillating speed is : [2025]