Waves Test

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Waves Test - 9

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Weekly Quiz Competition

Question 1
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A transverse wave travels on a taut steel wire with a velocity of $$v$$ when the tension in it is $$2.06\times { 10 }^{ 4 }N$$. When the tension is changed to $$T$$, the velocity changed to $$v/2$$. The value of $$T$$ is closet to:

A
$$2.50\times { 10 }^{ 4 }N$$

B
$$10.2\times { 10 }^{ 2 }N$$

C
$$30.5\times { 10 }^{ 4 }N\quad $$

D
$$5.15\times { 10 }^{ 3 }N$$

Solution

Velocity of sound in a medium
$$v = \sqrt{\dfrac{T}{\mu}}$$

$$v \propto \sqrt{T}$$

$$\Rightarrow \dfrac{v_1}{v_2} = \sqrt{\dfrac{T_1}{T_2}}$$

Given $$T_1 = 2.06 \times 10^4N$$

$$v_2 = \dfrac{v}{2}$$

$$v_1 = v$$

$$\dfrac{v}{v/2} = \sqrt{\dfrac{2.06\times 10^4}{T}}$$

$$4 = \dfrac{2.06\times 10^4}{T}$$

$$T = .515 \times 10^4 N$$

$$T = 5.15 \times 10^3N$$
Question 2
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The displacement of a particle varies according to the relation $$x = 4(\cos \pi t + \sin \pi t)$$. The amplitude of the particle is

A
$$-4$$

B
$$4$$

C
$$4\sqrt{2}$$

D
$$8$$

Solution

When the displacement , $$x=a\cos wt+b\sin wt$$, the amplitude will be $$A=\sqrt{a^2+b^2}$$
Here, $$a=4, b=4$$ so $$A=\sqrt{4^2+4^2}=4\sqrt 2$$
Question 3
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Amplitude of a wave is represented by $$A = \dfrac {c}{a + b - c}$$. Then resonance will occur when

A
$$b = -c/ 2$$

B
$$b = 0$$ and $$a = c$$

C
$$b = -a/2$$

D
None of the above

Solution

$$A = \dfrac {c}{a + b - c}$$: when $$b = 0, a = c$$
Amplitude $$A \rightarrow \infty$$. This correspondence to resonance.
Question 4
1 / -0

A simple wave motion represented by $$y=5(\sin 4\pi t+\sqrt 3 \cos 4\pi t)$$. Its amplitude is:

A
$$5$$

B
$$5\sqrt 3$$

C
$$10\sqrt 3$$

D
$$10$$

Solution

$$y=5(sin4\pi t +\sqrt{3}cos4\pi t)$$
$$=5\times 2(\dfrac{1}{2}sin4\pi t+\dfrac{\sqrt{3}}{2}cos4\pi t)$$
$$=10(cos\dfrac{\pi}{3}sin4\pi t+sin\dfrac{\pi}{3}cos4\pi t)$$
$$=10sin(4\pi t+\dfrac{\pi}{3})$$
Hence the amplitude of the wave is $$10$$.
Question 5
1 / -0

The phase change between incident and reflected sound wave from a free end is

A
$$0$$

B
$$\pi $$

C
$$3\pi $$

D
$$2\pi $$

Solution

At a free and, the wave is reflected as it is with just as change in its direction of propagation
$$y= A \sin ( \omega t+kx)$$
$$y_r= A \sin (\omega t-kx)$$
phase difference in time domain $$= 0$$
Question 6
1 / -0

Which of the following is conserved when light waves interfere?

A
momentum

B
amplitude

C
energy

D
intensity

Solution

when light waves interfere energy is conserved. During interference energy is simply redistributed. Option C is correct.
Question 7
1 / -0

Thickness of very thin films can be found by the technique of

A
Dispersion

B
Interference

C
polarization

D
Diffraction

Solution

Ellipsometry is a technique that is used to measure properties of thin film.
Ellipsometry uses the phenomenon of interference for the technique.
Thus option B is correct answer.
Question 8
1 / -0

Phase difference between a particle at a compression and a particle at the next rarefaction is

A
Zero

B
$$\dfrac{\pi}{2}$$

C
$$\pi$$

D
$$\dfrac{\pi}{4}$$

Solution

Phase difference between two successive compression of rarefaction is $$2\pi $$
As rarefaction appears between two compression, phase difference is $$\pi $$.
Question 9
1 / -0

Two light waves are represented by $$y_{1}=4\sin \omega t$$ and $$y_{2}= 3\sin(\omega t+\frac{\pi }{2} ) $$ . The resultant amplitude due to interference will be

A
$$5cm$$

B
$$7cm$$

C
$$1cm$$

D
$$0$$

Solution

The two waves are $$y_{1}=4\sin \omega t$$ and $$y_{2}=3\cos \omega t$$, the resultant wave $$y=y_{1}+y_{2}$$
$$=4\sin \omega t + 3\cos \omega t$$.
The resultant amplitude $$=\sqrt{4^{2}+3^{2}}$$
$$=\sqrt{25}=5$$
Question 10
1 / -0

For the sustained interference of light, the necessary condition is that the two sources should

A
have constant phase difference only

B
be narrow

C
be close to each other

D
of same amplitude with constant phase difference

Solution

Interference refers to the interaction of waves that are coherent with each other , either because they come from the same source of because they have
the same of nearly the same frequency. Thus option D is the correct option.

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Re-Attempt Weekly Quiz Competition

Waves Test - 9

Result

Waves Test - 9

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SHARING IS CARING

Question 1

$$2.50\times { 10 }^{ 4 }N$$

$$10.2\times { 10 }^{ 2 }N$$

$$30.5\times { 10 }^{ 4 }N\quad $$

$$5.15\times { 10 }^{ 3 }N$$

Solution

Question 2

$$-4$$

$$4$$

$$4\sqrt{2}$$

$$8$$

Solution

Question 3

$$b = -c/ 2$$

$$b = 0$$ and $$a = c$$

$$b = -a/2$$

None of the above

Solution

Question 4

$$5$$

$$5\sqrt 3$$

$$10\sqrt 3$$

$$10$$

Solution

Question 5

$$0$$

$$\pi $$

$$3\pi $$

$$2\pi $$

Solution

Question 6

momentum

amplitude

energy

intensity

Solution

Question 7

Dispersion

Interference

polarization

Diffraction

Solution

Question 8

Zero

$$\dfrac{\pi}{2}$$

$$\pi$$

$$\dfrac{\pi}{4}$$

Solution

Question 9

$$5cm$$

$$7cm$$

$$1cm$$

$$0$$

Solution

Question 10

have constant phase difference only

be narrow

be close to each other

of same amplitude with constant phase difference

Solution

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