Waves Test

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Waves Test - 50

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Weekly Quiz Competition

Question 1
1 / -0

The amplitude of a wave disturbance propagating in the positive y-direction is given by:
$$y = \dfrac{1}{1 + x^2}$$ at $$ t = 0s \ and \ y = \dfrac{1}{1 + (x - 1)^2}$$ at $$ t = 2s$$, then wave velocity is

A
$$1 m/s$$

B
$$1.5 m/s$$

C
$$0.5 m/s$$

D
$$2 m/s$$

Solution

in $$2$$ sec the wave moves $$1$$m
$$\therefore$$Velocity $$ = \dfrac{1}{2}\,\,m/s$$.
$$\therefore$$ Option $$C$$ is correct.
Question 2
1 / -0

The light waves from two independent monochromatic light sources are given by-
$${y_1} = 2\sin {\omega t }$$ and $${y_2} = 2\cos {\omega t }$$,
then the following statement is correct

A
Both the waves are coherent

B
Both the waves are incoherent

C
Both the waves have different time periods

D
None of the above

Solution

$${y_1} = 2\sin \left( {\omega t - kx} \right)$$
$${y_2} = 2\cos \left( {\omega t - kx} \right) = 2\sin \left( {\omega t - kx + \frac{\pi }{2}} \right)$$
So, Phase difference = $$\frac{\pi}{2}$$
Hence sources are incoherent.
Question 3
1 / -0

The displacement of a particle executing S.H.M is given by $$x=0.25sin200t$$in meters.The maximum speed of particle is :

A
$$50m{s^{ - 1}}$$

B
$$25m{s^{ - 1}}$$

C
$$200m{s^{ - 1}}$$

D
$$100m{s^{ - 1}}$$

Solution

$$\begin{array}{l}{V_{\max }} = Aw\\when\,\cos wt = 1\\x = 0.25\cos \left( {200t} \right)\\{V_{\max }} = 0.25 \times 200 = 50m{s^{ - 1}}\end{array}$$
Question 4
1 / -0

The displacements of two interfering light waves are $$y_1 = 4 \ sin (\omega t) \ and \ y_2 = 3 \ cos (\omega t).$$ The amplitude of the resultant wave is ($$y_1$$ and $$y_2$$ are in CGS system)

A
$$5 cm$$

B
$$7 cm$$

C
$$1 cm$$

D
$$zero$$

Solution

$$y_{1}=A \sin{(\omega t)}$$
$$y_{2}=3 \sin{(\omega t)}$$
Amplitude of first wave=$$y_{1}=4=A_{1}$$
Amplitude of second wave=$$A_{2}=3$$
Resultant=$$\sqrt{(4)^{2}+(3)^{2}}=\sqrt{16+9}=5cm$$
Question 5
1 / -0

The same progressive wave is represented by two graphs $$I$$ and $$II$$. Graph $$I$$ shows how the displacement $$'y'$$ varies with the distance $$x$$ along the wave at a given time. Graph $$II$$ shoes how $$y$$ varies with time $$t$$ at a given point on the wave. The ratio measurements $$AB$$ to $$CD$$, marked on the curves, represents:

A
Wave number $$k$$

B
Wave speed $$V$$

C
Frequency $$v$$.

D
Angular frequency $$\omega$$

Solution
Question 6
1 / -0

Two $$SHM$$ are represented by equation $$x_{1}=4\ \sin (\omega t+37^{o})$$ and $$x_{2}=5\ \cos (\omega t)$$. The phase difference between them is

A
$$37^{o}$$

B
$$127^{o}$$

C
$$53^{o}$$

D
$$143^{o}$$

Solution

Given,

$$ x=A\sin (\omega t+\phi ),\,\, $$

$$ where,\,\, $$

$$ A=$$ Amplitude

$$ \phi =$$ Phase Angle

$${{x}_{1}}=4\ \sin (\omega t+{{37}^{o}})\,\ldots \ldots \,(1)$$

$${{x}_{2}}=5\ \cos \text{ }\!\!~\!\!\text{ }(\omega t)=5\sin (\omega t+{{90}^{o}})\,\ldots \ldots \,(2)$$

Phase angle difference is $${{90}^{o}}-{{37}^{o}}={{53}^{o}}$$
Question 7
1 / -0

Two sources of waves are called coherent if:-

A
Both have the same amplitude of vibrations

B
Both produce waves of the same wavelength

C
Both produce waves of the same wavelength having constant phase difference

D
Both produce waves having the same velocity

Solution

$$\textbf{Explanation:}$$ Coherent source of light are those sources which emit a light wave having the same frequency, wavelength and in the same phase or they have a constant phase difference

Hence (c) option is correct
Question 8
1 / -0

The wave number of energy emitted when electron jumps from fourth orbit to seconds orbit in hydrohen in $$20,497\ cm^{-1}$$. The wave number of energy for the same transition in $$He^{+}$$ is

A
$$5,099\ cm^{-1}$$

B
$$20,497\ cm^{-1}$$

C
$$40,994\ cm^{-1}$$

D
$$81,988\ cm^{-1}$$

Solution

Given that,

Wave number of energy for hydrogen $$=20497\,c{{m}^{-1}}$$

Now, for hydrogen

$$\dfrac{1}{{{\lambda }_{H}}}=R\left( \dfrac{1}{{{2}^{2}}}-\dfrac{1}{{{4}^{2}}} \right)=20497$$

Now, for helium

$$ \dfrac{1}{\lambda }=R\left( \dfrac{1}{{{2}^{2}}}-\dfrac{1}{{{4}^{2}}} \right)\times {{2}^{2}} $$

$$ \dfrac{1}{{{\lambda }_{He}}}=20497\times 4 $$

$$ \dfrac{1}{{{\lambda }_{He}}}=81988\,c{{m}^{-1}} $$

Hence, the wave number of energy for helium is $$81988\ cm^{-1}$$
Question 9
1 / -0

A particle is performing simple harmonic motion bout its equilibrium position $$X_0$$, then

A
$$X_0$$ must be zero

B
velocity of particle at $$X_0$$ may be zero

C
acceleration of particle at $$X_0$$ may be zero

D
acceleration of particle at $$X_0$$ must be zero

Solution

Aparticle is performing simple harmonic motion bout its equilibrium position
$$X_0$$ then
$$a=\cfrac{d^2x}{dt^2}\\ \quad=\cfrac{d^2x_0}{dt^2}$$
Due to its equilibrium position $$X_0$$ the velocity will be uniform. hence
acceleration is $$\cfrac{V_2-V_1}{t}=1=a$$
$$V_2=$$ Final velocity
$$V_1=$$ Initial velocity
$$t=$$ time internal
Question 10
1 / -0

from a line source, if amplitude of a wave at a a distance r is A, then the amplitude at a distance 4r will be

A
2A

B
A

C
A/2

D
A/4

Solution

$$\begin{array}{l} I\left( { { { intensity } } } \right) \times \frac { 1 }{ { { r^{ 2 } } } } \\ I\times { A^{ 2 } } \\ \therefore ,\, \, A\times \frac { 1 }{ r } \\ if\, \, r\to 4r,A\to \frac { A }{ 4 } \end{array}$$

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Waves Test - 50

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Waves Test - 50

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SHARING IS CARING

Question 1

$$1 m/s$$

$$1.5 m/s$$

$$0.5 m/s$$

$$2 m/s$$

Solution

Question 2

Both the waves are coherent

Both the waves are incoherent

Both the waves have different time periods

None of the above

Solution

Question 3

$$50m{s^{ - 1}}$$

$$25m{s^{ - 1}}$$

$$200m{s^{ - 1}}$$

$$100m{s^{ - 1}}$$

Solution

Question 4

$$5 cm$$

$$7 cm$$

$$1 cm$$

$$zero$$

Solution

Question 5

Wave number $$k$$

Wave speed $$V$$

Frequency $$v$$.

Angular frequency $$\omega$$

Solution

Question 6

$$37^{o}$$

$$127^{o}$$

$$53^{o}$$

$$143^{o}$$

Solution

Question 7

Both have the same amplitude of vibrations

Both produce waves of the same wavelength

Both produce waves of the same wavelength having constant phase difference

Both produce waves having the same velocity

Solution

Question 8

$$5,099\ cm^{-1}$$

$$20,497\ cm^{-1}$$

$$40,994\ cm^{-1}$$

$$81,988\ cm^{-1}$$

Solution

Question 9

$$X_0$$ must be zero

velocity of particle at $$X_0$$ may be zero

acceleration of particle at $$X_0$$ may be zero

acceleration of particle at $$X_0$$ must be zero

Solution

Question 10

2A

A

A/2

A/4

Solution

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