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Waves MCQs for NEET — Physics Questions with Answers

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The disc of a siren containing 60 holes rotates at a constant speed of 360 rpm. The emitted sound is in unison with a tuning fork of frequency :

10 Hz

360 Hz

216 Hz

6 Hz

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Explanation

Frequency $= \frac{360}{60} \times 60 = 360 H z .$

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The distance between the nearest node and antinode in a stationary wave is :

$\frac{λ}{2}$

$\frac{λ}{4}$

2λ

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Explanation

In a stationary wave, nodes are points of zero displacement, and antinodes are points of maximum displacement. The distance between a node and an adjacent antinode is one-quarter of the wavelength (Î»/4). Therefore, the correct answer is (Î»/4).

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For the stationary wave $y = 4 \sin (\frac{π x}{15}) \cos (96 π t)$ , the distance between a node and the next antinode is :

7.5

22.5

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Explanation

Comparing given equation with standard equation

$y = 2 a \sin \frac{2 π x}{λ} \cos \frac{2 π v t}{λ}$ gives us $\frac{2 π}{λ} = \frac{π}{15} \Rightarrow λ = 30$

Distance between nearest node and antinodes = $\frac{λ}{4} = \frac{30}{4} = 7 .5$

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The equation of a stationary wave is $y = 0 .8 \cos (\frac{π x}{20}) \sin 200 π t$ , where x is in cm and t is in sec. The separation between consecutive nodes will be :

20 cm

10 cm

40 cm

30 cm

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Explanation

On comparing the given equation with the standard equation $y = 2 a \sin \frac{2 π x}{λ} \cos \frac{2 π v t}{λ}$

We get $\frac{2 π}{λ} = \frac{π}{20} \Rightarrow λ = 40$

The separation between two consecutive nodes = $\frac{λ}{2} = \frac{40}{2} = 20 c m$

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A wave represented by the given equation $y = a \cos (k x - ω t)$ is superposed with another wave to form a stationary wave such that the point x = 0 is a node. The equation for the other wave is :

$y = a \sin (k x + ω t)$

$y = - a \cos (k x + ω t)$

$y = - a \cos (k x - ω t)$

$y = - a \sin (k x - ω t)$

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Explanation

Since the point x = 0 is a node and reflection is taking place from point x = 0. This means that reflection must be taking place from the fixed end and hence the reflected ray must suffer an additional phase change of π or a path change of $\frac{λ}{2}$ .

So, if $y_{incident} = a \cos (k x - ω t)$

⇒ $y_{reflected} = a \cos (- k x - ω t + π) = - a \cos (ω t + k x)$

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A standing wave having 3 nodes and 2 antinodes is formed between two atoms having a distance 1.21 Å between them. The wavelength of the standing wave is :

1.21 Å

2.42 Å

6.05 Å

3.63 Å

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In stationary waves, the distance between a node and its nearest antinode is 20 cm. The phase difference between two particles having a separation of 60 cm will be :

Zero

π/2

3π/2

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Explanation

$\frac{λ}{4} = 20 \Rightarrow λ = 80 c m$ , also $Δ ϕ = \frac{λ}{2 π} . Δ x$

⇒ $Δ ϕ = \frac{60}{80} \times 2 π = \frac{3 π}{2}$

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A standing wave is represented by

$Y = A \sin (100 t) \cos (0 .01 x)$

where Y and A are in millimetre, t is in seconds and x is in metre. The velocity of the wave is :

10⁴ m/s

1 m/s

10^–4m/s

Not derivable from the above data

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Explanation

By comparing given equation with $y = a \sin (ω t) \cos k x$

⇒ $v = \frac{ω}{k} = \frac{100}{0 .01} = 10^{4} m / s$

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Two waves are approaching each other with a velocity of 20 m/s and frequency n. The distance between two consecutive nodes is :

$\frac{20}{n}$

$\frac{10}{n}$

$\frac{5}{n}$

$\frac{n}{10}$

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Explanation

Distance between the consecutive node $= \frac{λ}{2},$

but $λ = \frac{v}{n} = \frac{20}{n}$ so $\frac{λ}{2} = \frac{10}{n}$

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The stationary wave produced on a string is represented by the equation $y = 5 \cos (π x / 3) \sin 40 π t$ where x and y are in cm and t is in seconds. The distance between consecutive nodes is :

5 cm

π cm

3 cm

40 cm

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Explanation

On comparing the given equation with standard equation $\Rightarrow \frac{2 π}{λ} = \frac{π}{3} \Rightarrow λ = 6 c m$ .

Hence, distance between two consecutive nodes ⇒ λ = 3 cm

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