Waves Test

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Waves Test - 39

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Weekly Quiz Competition

Question 1
1 / -0

During the propagation of wave motion,

A
there is transfer of energy from one particle to another without any actual transfer of the particles of the medium.

B
there is transfer of energy from one particle to another with transfer of the particles of the medium.

C
there is no transfer of energy from one particle to another.

D
None of these.

Solution

during propagation of waves energy is transferred from one particle to to another without transfer of particles.
so the answer is A.
Question 2
1 / -0

A particle in SHM is described by the displacement function: $$x(t)= A \ cos (\omega t+ \phi).$$ If the initial (t=0) position of the particle is 1 cm and its initial velocity is $$\pi $$ cm/sec , what is the amplitude?

A
$$\sqrt 2 cm $$

B
$$ 2 cm $$

C
$$\sqrt 7 cm $$

D
$$12 cm $$

Solution

$$x(t)=Acos(\omega t+\phi)$$
$$\implies v(t)=\dfrac{dx(t)}{dt}$$
$$=-\omega Asin(\omega t+\phi)$$
Initial position=$$x(t=0)=Acos\phi=1cm$$
Initial velocity=$$v(t=0)=-A\omega sin\phi=\omega cm/s$$
Hence, $$A=\sqrt{2}cm$$
Question 3
1 / -0

The wave carries ______________

A
Power

B
Energy

C
Displacement

D
Work

Solution

wave carries energy ,as propagation of wave is propagation of energy .
so the answer is B.
Question 4
1 / -0

Which of the following is a Longitudinal wave? _____________

A
Radio wave

B
X-rays

C
Light waves

D
Sound waves

Solution

the example of longitudinal waves is sound waves rest three are transverse in nature.
so the answer is D.
Question 5
1 / -0

The displacement y of a wave traveling in the X-direction is given by $$y = 10^{-4}\sin({600t-2x+\dfrac{\pi}{3})}$$ metres. where $$x$$ is expressed in metres and $$t$$ in $$seconds$$. The speed of the wave motion in $$ms^{-1}$$ is:

A
$$200$$

B
$$300$$

C
$$600$$

D
$$1200$$

Solution

$$y={ 10 }^{ -4 }sin\left( 600t-2x+\dfrac { \pi }{ 3 } \right) $$
Here, $$W=600/s$$
$$K=2/m$$
Speed of wave $$V=W/K$$
$$=600/2$$
$$=300m/s$$

$$\therefore $$ Option (B) is correct.
Question 6
1 / -0

An excerpt from a book by Einstein and Infeld gives the following remarks concerning wave phenomena:
"A bit of gossip starting in Washington reaches New York [by word of mouth] very quickly, even though not a single individual who takes part in spreading it travels between these two cities. There are two quite different motions involved, that of the rumor, Washington to New York, and that of the persons who spread the rumor."

Identify a correct inference from the above text.

A
The particles of the medium perform motion from one place to another.

B
The particles of the medium perform random motion to constitute wave motion.

C
The particles constituting the medium perform only small vibrations, but the whole motion is that of a progressive wave.

D
None of these.

Solution

Sound waves are longitudinal waves, the particle itself do not travel from one place to other, they only vibrates in their positions and only energy is being transferred from one particle to other.
Hence option (C) is correct.
Question 7
1 / -0

Three waves of amplitudes $$ 12\mu m $$, $$ 4\mu m $$ and $$ 9\mu m $$ but of same frequency arrive at a point in a medium with a successive phase diffeerence of $$\dfrac{\pi}{2}$$. Then the resultant amplitude is

A
$$4$$

B
$$7$$

C
$$5$$

D
$$25$$

Solution

Since three waves have a successive phase difference of $$\pi/2$$.
So, first and third waves have phase difference of $$\pi$$.
Thus, net amplitude of first and third wave is $$A_1 = 12-9 = 3\mu m$$
Amplitude of second wave $$A_2 = 4\mu m $$
Resultant amplitude $$A_R = \sqrt{A_1^2 + A_2^2}$$
$$\therefore$$ $$A_R = \sqrt{3^2 + 4^2} = 5\mu m$$
Question 8
1 / -0

A traveling wave in a stretched string is described by the equation, $$y = A \sin(kx+t)$$. The maximum particle velocity is

A
A

B
$$k$$

C
$$Ak$$

D
none of the above

Solution

$$v=\dfrac{dy}{dt}=Acos(kx+t)$$
Since the max value of $$cos$$ is 1.
The maximum velocity is $$A$$.
Question 9
1 / -0

Two sound waves each of amplitude $$a$$ and of frequencies $$500 Hz$$ and $$512 Hz$$ superpose. Then the resultant of the amplitude of the resultant wave at $$t=\dfrac{5}{48} s$$ is

A
$$0$$

B
$$\dfrac { a }{ \sqrt { 2 } } $$

C
$$a\sqrt { 2 } $$

D
$$2a$$

Solution

When two sound waves of slightly different frequencies and equal amplitudes superimpose on each other, then their resultant amplitude is given by
$$R= 2a\cos(2\pi\dfrac{n_1-n_2}{2}t)=2a\cos(2\pi\times\dfrac{512-500}{2}\times\dfrac{5}{48})=\dfrac{a}{\sqrt2}$$
Note that here the angle is in radians.
Substitute and calculate.
Question 10
1 / -0

If two waves of length $$50 cm$$ and $$51 cm$$ produced $$12$$ beats $$per\ second$$, the velocity of sound is:

A
$$360$$

B
$$340$$

C
$$306$$

D
none of the above

Solution

Given,
Wavelength,
$${ \lambda }_{ 1 }=50cm=0.5m\\ { \lambda }_{ 2 }=51cm=0.51m$$
Frequency of the beats, f=12
Now, $$f=\frac { V }{ { \lambda }_{ 1 } } -\frac { V }{ { \lambda }_{ 2 } } =V\left[ \frac { 1 }{ { \lambda }_{ 1 } } -\frac { 1 }{ { \lambda }_{ 2 } } \right] \\ 12=V\left[ \frac { 1 }{ 0.5 } -\frac { 1 }{ 0.51 } \right] \\ 12=V\left[ \frac { 0.01 }{ 0.5\times 0.51 } \right] \\ \left[ V=306m/s \right] $$
Hence option (C) is correct

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Re-Attempt Weekly Quiz Competition

Waves Test - 39

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Waves Test - 39

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SHARING IS CARING

Question 1

there is transfer of energy from one particle to another without any actual transfer of the particles of the medium.

there is transfer of energy from one particle to another with transfer of the particles of the medium.

there is no transfer of energy from one particle to another.

None of these.

Solution

Question 2

$$\sqrt 2 cm $$

$$ 2 cm $$

$$\sqrt 7 cm $$

$$12 cm $$

Solution

Question 3

Power

Energy

Displacement

Work

Solution

Question 4

Radio wave

X-rays

Light waves

Sound waves

Solution

Question 5

$$200$$

$$300$$

$$600$$

$$1200$$

Solution

Question 6

The particles of the medium perform motion from one place to another.

The particles of the medium perform random motion to constitute wave motion.

The particles constituting the medium perform only small vibrations, but the whole motion is that of a progressive wave.

None of these.

Solution

Question 7

$$4$$

$$7$$

$$5$$

$$25$$

Solution

Question 8

A

$$k$$

$$Ak$$

none of the above

Solution

Question 9

$$0$$

$$\dfrac { a }{ \sqrt { 2 } } $$

$$a\sqrt { 2 } $$

$$2a$$

Solution

Question 10

$$360$$

$$340$$

$$306$$

none of the above

Solution

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