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Waves MCQs for NEET — Physics Questions with Answers

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A transverse wave of amplitude 0.5 m and wavelength 1 m and frequency 2 Hz is propagating in a string in the negative x-direction. The expression for this wave is :

$y (x, t) = 0 .5 \sin (2 π x - 4 π t)$

$y (x, t) = 0 .5 \cos (2 π x + 4 π t)$

$y (x, t) = 0 .5 \sin (π x - 2 π t)$

$y (x, t) = 0 .5 \cos (2 π x + 2 π t)$

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Explanation

$∵ y = a \cos (\frac{2 π}{λ} v t + \frac{2 π x}{λ}) = 0 .5 \cos (4 π t + 2 π x)$

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The displacement of a particle is given by $y = 5 \times 10^{- 4} \sin (100 t - 50 x)$ , where x is in meter and t is in sec, find out the velocity of the wave :

5000 m/sec

2 m/sec

0.5 m/sec

300 m/sec

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Explanation

$v = \frac{Co-efficient of t}{Co-efficient of x} = \frac{100}{50} = 2 m / \sec$ .

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Which one of the following does not represent a traveling wave :

$y = \sin (x - v t)$

$y = y_{m} \sin k (x + v t)$

$y = y_{m} \sin (x - v t)$

$y = f (x^{2} - v t^{2})$

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Explanation

$y = f (x^{2} - v t^{2})$ doesn’t follows the standard wave equation.

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Wave equations of two particles are given by $y_{1} = a \sin (ω t - k x)$ , $y_{2} = a \sin (k x + ω t)$ , then :

They are moving in the opposite direction

The phase between them is 90°

The phase between them is 180°

The phase between them is 0°

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Explanation

Both waves are moving opposite to each other .

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A transverse wave is represented by the equation $y = y_{0} \sin \frac{2 π}{λ} (v t - x)$

For what value of λ, the maximum particle velocity equal to two times the wave velocity?

$λ = 2 π y_{0}$

$λ = π y_{0} / 3$

$λ = π y_{0} / 2$

$λ = π y_{0}$

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Explanation

On comparing the given equation with standard equation $y = a \sin \frac{2 π}{λ} (v t - x)$ , it is clear that

wave speed ${(v)}_{w a v e} = v$ and

maximum particle velocity ${(v_{\max})}_{p a r t i c l e} = a ω = y_{0} \times$ coefficient of t $= y_{0} \times \frac{2 π v}{λ}$

$∵ {(v_{\max})}_{p a r t i c l e} = 2 {(v)}_{w a v e}$ ⇒ $\frac{a \times 2 π v}{λ} = 2 v$ ⇒ $λ = π y_{0}$

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A wave travels in a medium according to the equation of displacement given by $y (x, t) = 0 .03 \sin π (2 t - 0 .01 x)$ where y and x are in metres and t in seconds. The wavelength of the wave is :

200 m

100 m

20 m

10 m

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Explanation

Comparing with $y = (x, t) = a \sin (ω t - k x)$

$k = \frac{2 π}{λ} = 0 .01 π$ ⇒ λ = 200 m.

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Equation of a progressive wave is given by $y = 4 \sin \{π (\frac{t}{5} - \frac{x}{9}) + \frac{π}{6}\}$

Then which of the following is correct ?

v = 5 m / sec

λ = 18 m

a = 0.04 m

n = 50 Hz

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Explanation

From the given equation amplitude $a = 4 m$

Frequency $= \frac{Co - efficient of t}{2 π} = \frac{π / 5}{2 π} = \frac{1}{10} H z$

Wave length $λ = \frac{2 π}{Co - efficient o f x} = \frac{2 π}{π / 9}$ =18m.

Wave speed $v = \frac{Co-efficient of t}{Co-efficient of x} = \frac{π / 5}{π / 9} = 1 .8 m / s .$

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The frequency of the sinusoidal wave $y = 0 .40 \cos [2000 t + 0 .80 x]$ would be :

1000 π Hz

2000 Hz

20 Hz

$\frac{1000}{π} H z$

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Explanation

Compare the given equation with $y = a \cos (ω t + k ϕ)$

⇒ $ω = 2 π n = 2000$ ⇒ $n = \frac{1000}{π} H z$

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The equation of a plane progressive wave is given by $y = 0 .025 \sin (100 t + 0 .25 x)$ . The frequency of this wave would be :

$\frac{50}{π} H z$

$\frac{100}{π} H z$

100 Hz

50 Hz

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Explanation

Compare the given equation with $y = a \sin (ω t + k x)$ . We get $ω = 2 π n = 100$ ⇒ $n = \frac{50}{π} H z$

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In the given progressive wave equation, what is the maximum velocity of particle $Y = 0 .5 \sin (10 π t - 5 x)$ cm

5 cm/s

5π cm/s

10 cm/s

10.5 cm/s

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Explanation

Maximum velocity of the particle

$v_{\max} = a ω = 0 .5 \times 10 π = 5 π c m / s e c$

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