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Travelling waves - class-XI

Description: travelling waves
Number of Questions: 41
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Tags: wave motion oscillation and waves properties of waves sound physics waves oscillations and waves
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Crest or troughs in a travelling wave are

  1. moving entities

  2. stationary entitites

  3. moving entities along +Y direction

  4. moving entities along -Y direction


Correct Option: A
Explanation:

Crest and troughs are part of the waves and they will be  moving in the direction of the wave

The correct option is (a)

The distance between two consecutive crests or troughs are equal in a wave

  1. True

  2. False


Correct Option: A
Explanation:

The distance between two consecutive crests or troughs are equal in a wave and is known as the length of a wave or wavelength

Ocean waves of time period $0.01$ second have a speed $15 m/s$. What is the adjacent crest and the trough is:

  1. $15 \times 10^{-2} m$

  2. $7.5 \times 10^{-2} m$

  3. $3.25 \times 10^{-2} m$

  4. $30 \times 10^{-2} m$


Correct Option: B

The velocity of light in glass whose refractive index w.r.t air is $1.5$ is $2 \times 10^8 \,m/s$. In a certain liquid, the velocity of light is found to be $2.5 \times 10^8 \,m/s$. The refractive index of the liquid w.r.t air is

  1. $0.8$

  2. $0.9$

  3. $1.2$

  4. $1.33$


Correct Option: C
Explanation:
Velocity of light in glass $(v _1)=2\times 10^8 m/s$
Refractive index of glass $(\eta _1)=1.5$
w.r.t air
Velocity of light in certain $2\times 10^8\ m/s$
liquid $(v _2)$
Let refractive index of certain $=\eta _g$
liquid w.r.t air
Using formula,
$Refractive\ index=\dfrac{Velocity\ of\ light}{Velocity\ of\ light\ in\ med}$
we get
$\dfrac{\eta _1}{\eta _2}=\dfrac{V _2}{V _1}$
$\eta _2=\dfrac{\eta _1 V _1}{V _2} $
$\eta _2=\dfrac{31.5\times 2\times 10^8}{52.5\times 10^8}$
$\eta _2=\dfrac{6}{5}=1.2$
$\therefore$ Refractive index of certain liquid$=1.2$

If the distance between two successive troughs in a transverse wave is 8 cm, then the amplitude of that wave is 5 cm.

  1. True

  2. False


Correct Option: B
Explanation:

wavelength and amplitude are independent of each other so for any value of amplitude any wavelength can be possible .

so the answer  is B.

Water waves are:

  1. Longitudinal

  2. Transverse

  3. Both Longitudinal and transverse

  4. Neither longitudinal nor transverse


Correct Option: C
Explanation:

The water molecules displace along the propagation direction as well as along perpendicular direction. 

Hence, water waves are both longitudinal and transverse.

A transverse wave travelling on a taut string is represented by $y = 0.01 \sin 2 \pi ( 10 t - x )$ where y and x are in metre and t is in second. Then

  1. The speed of the wave is 10 m/s.

  2. Closest points on the string which differ in phase by $60^o$ are $\dfrac16\ m$ apart.

  3. Maximum particle speed is $\frac { \pi } { 5 } { m } / { s }$

  4. The phase of a certain point on the string changes by $120 ^ { \circ }$ is $\dfrac1{20} $seconds


Correct Option: A,B

What is the phase difference between two successive crests in the wave?

  1. $\pi$

  2. $\frac{\pi}{2}$

  3. $2\pi$

  4. $4\pi$


Correct Option: C
Explanation:

Phase difference between any two particles in a wave determines lack of harmony in the vibrating state of two particles, ie, how far one particle leads the other or lags behind the other. 
Relation of path difference and phase difference is given by
$\Delta \phi=\frac{2\pi}{\lambda}\times \Delta x$
where $\Delta x$ is path difference. 
But path difference between two crests
$\Delta x=\lambda$
Hence, $\Delta  \phi = \frac{2\pi}{\lambda}\times \lambda =2\pi$ 

The wave produced by a motor boat sailing in water are

  1. Transverse

  2. Longitudinal

  3. Longitudinal and Transverse

  4. Stationary


Correct Option: C
Explanation:

The waves produced by a motorboat sailing in water are of both transverse and longitudinal type. Transverse waves are produced on the surface and longitudinal waves are produced deep inside the water.

A crest is the point of maximum displacement of a particle in a wave. State whether true or false.

  1. True

  2. False


Correct Option: A
Explanation:

A crest is a point on the wave with the maximum value of upward displacement within a cycle. A crest is a point on the surface wave where the displacement of the medium is the maximum.

Transverse mechanical wave can travel in

  1. Iron rod

  2. Hydrogen gas

  3. Water surface

  4. Stretched string


Correct Option: A,C,D
Explanation:

Transverse waves can travel only in solids and only along the surface of liquids, but not in the entire liquid. They can't travel in gases.

Since iron rod and stretched string are solids, transverse waves can travel in them.
Water surface being a liquid surface they can travel in it also.
Hydrogen gas being a gas, they can't travel in it.

Which of the following can travel through vacuum?

  1. Light waves

  2. Heat waves

  3. $X$-rays

  4. Sound waves


Correct Option: A,B,C
Explanation:

Heat rays are infra-red rays.

Light rays, infra-red rays and X-rays are all electromagnetic rays.
Electromagnetic rays can travel through vacuum and through transperent media.
However, sound waves are mechanical longitudinal waves. They need a material medium for travelling. They can't travel through vacuum.

Which of the following does not identify a necessary property of wave motion?

  1. transmission of energy

  2. periodic motion

  3. disturbance

  4. a material medium


Correct Option: D
Explanation:

In any wave motion, energy is always transferred to the next particle which is succeeding the previous particle.  In a wave motion, particles are oscillating in a direction perpendicular to the direction of propagation or parallel. Since oscillation is a periodic motion,  we can say that periodic motion is always associated with the wave.  An oscillatory disturbance is always imparted the next and next particle and this is how the disturbance Travels across the particles.  Ordinary waves require a material medium for propagation. But electromagnetic waves do not require any material medium. They can also propagate through vacuum. Thus material medium is not a necessary condition for all wave motions.

During propagation of a plane progressive mechanical wave :

  1. all the particles are vibrating in the same phase

  2. amplitude of all the particles is equal

  3. particles of the medium execute S.H.M.

  4. wave velocity depends upon the nature of the medium


Correct Option: B,C,D
Explanation:

During propagation of a plane progressive mechanical wave amplitude of all the particles is equal, particle of the medium execute S.H.M, wave velocity depends upon the nature of the medium and all the particles are vibrating in the different phase.

Hence $B, C$ and $D$ are correct options.

Distance between crest and through is

  1. $\displaystyle \frac{\lambda}{4}$

  2. $\displaystyle \frac{2\lambda}{6}$

  3. $\displaystyle \frac{\lambda}{2}$

  4. $\displaystyle \frac{2\lambda}{3}$


Correct Option: C

A point on the wave, wherein the displacement of the wave is ___________ is known as a crest

  1. Maximum

  2. Minimum

  3. Zero

  4. None of the above


Correct Option: A
Explanation:

crest is a point on the wave where the displacement of the medium is at a maximum

The correct option is (a)

A string tied to a wall is given a flip at the other end with an initial velocity u, which generates a curve. After sometime, this curve is seen to reach the wall with the same speed. The transfer of the kinetic energy takes place due to

  1. air molecules surrounding the string

  2. sound wave carried by the string

  3. molecules on the string

  4. none of the above


Correct Option: C
Explanation:

For the wave to propogate, it needs a mechanical medium and this uses the molecules of string to propogate the energy


The correct option is (c)

A heat energy of 540 kJ ,given to 1 litre of water at 100C makes the water to boil. In this process, heat energy is transferred from the source to water by means of 

  1. water

  2. steam

  3. air

  4. none of the above


Correct Option: A
Explanation:

Water acts as a medium to transfer heat energy from the source

The correct option is (a)

A metal hammer hits a spherical bell, when the circuit in a calling bell is switched ON, the propogation of sound takes place due to 

  1. Air

  2. electric current

  3. metal bell

  4. none of the above


Correct Option: A
Explanation:

Though the hammer strikes the bell and the bell starts vibrating, these vibrations are then carried out to the atmosphere only by air molecules thereby creating a sound

The correct option is (a)

Waves that are combination of longitudinal and transverse nature are

  1. water waves

  2. light waves

  3. shock waves

  4. sound waves


Correct Option: A
Explanation:

Water waves are an example of waves that involve a combination of both longitudinal and transverse motions. As a wave travels through the waver, the particles travel in clockwise circles. The radius of the circles decreases as the depth into the water increases. The animation at right shows a water wave travelling from left to right in a region where the depth of the water is greater than the wavelength of the waves. I have identified two particles in orange to show that each particle indeed travels in a clockwise circle as the wave passes.

Particles in the combination of longitudinal and transverse waves moves in 

  1. straight line

  2. circles

  3. rectangles

  4. vibrates


Correct Option: B
Explanation:

Particles move in circular paths at the surface of a medium and hence form at the boundary of two mediums.

The correct option is (b)

Waves created in Tsunami are

  1. Longitudinal waves

  2. Transverse waves

  3. Longitudinal and transverse waves

  4. Neither longitudinal or transverse


Correct Option: C
Explanation:

Tsunami waves are water waves and hence have both the elements of transverse and longitudinal.

Thus option (c) is the correct option

Two particles in a medium are vibrating with a path difference of $10$ m and corresponding time difference is $0.1$s. The speed of wave in the medium is?

  1. $100$ m/s

  2. $300$ m/s

  3. $50$ m/s

  4. $200$ m/s


Correct Option: A
Explanation:

Path difference=10m

time difference=0.1 sec

Speed= $\dfrac{10}{0.1} $ m/s

$=100$ m/s

A transverse wave travels along z-axis. The particles of the medium moves

  1. Along the z-axis

  2. Along the x-axis

  3. Along the y-axis

  4. In the x-y plane


Correct Option: D
Explanation:

The particles of medium moves perpendicular to the direction of the propagation of the wave in the case of transverse wave.

In the given question, a transverse wave travels along z-axis. All the lines in the X-Y plane are perpendicular to z-axis, hence the particle of the medium must move in the X-Y plane.
The correct option is D.

The particle displacement of a travelling longitudinal wave is represented by S=S (x,t). The midpoints of a compression zone and an adjacent rarefaction zone are represented by the letter 'C' and 'R' Which of the following is true?

  1. ${ \left| \partial S/\partial x \right| } _{ C }={ \left| \partial S/\partial x \right| } _{ R }$

  2. ${ \left| \partial S/\partial t \right| } _{ C }={ \left| \partial S/\partial t \right| } _{ R }=0$

  3. ${ \left( pressure \right) } _{ C }-{ \left( pressure \right) } _{ R }=2{ \left| \partial S/\partial x \right| } _{ C }x$ Bulk modulus of air.

  4. Particles of air are stationary mid-way between 'C' and 'R'.


Correct Option: A

The equation of a transverse wave travelling in a rope is given by $y = 5\sin (4t - 0.02x)$, where $y$ and $x$ are in cm and time $t$ is in second.
Then the maximum transverse speed of wave in the rope is

  1. $125\ cm/s$

  2. $200\ cm/s$

  3. $250\ cm/s$

  4. $100\ cm/s$


Correct Option: B

Two small boats are $10m$ apart on a lake. Each pops up and down with a period of $4.0 seconds$ due to wave motion on the surface of water. When one boat is at its highest point, the other boat is at its lowest point. Both boats are always within a single cycle of the waves. The speed of the waves is:

  1. $2.5m/s$

  2. $5.0m/s$

  3. $14m/s$

  4. $40m/s$


Correct Option: B

Disturbance $y(x, t)$ of a wave propagating in the position x-direction is given by $y = \dfrac {1}{1 + x^{2}}$ at time $t = 0$ and by $y = \dfrac {1}{[1 + (x - 1^{2})]}$ at $t = 2\ s$, where $x$ and $y$ are in meters. The shape of the wave disturbance does not change during the propagation. The velocity of wave in m/s is

  1. $2.0$

  2. $4.0$

  3. $0.5$

  4. $1.0$


Correct Option: B

In gases which wave cannot propagate

  1. standing wave

  2. longitudinal wave

  3. transverse wave

  4. none


Correct Option: C
Explanation:

Transverse waves cannot propagate in gases because there are no forces to cause motion perpendicular to the direction of the wave. A transverse wave propagates in a solid because each atom of the solid has an "equilibrium location" where the forces on it from all its neighboring atoms balance. If one atom is pulled out of its equilibrium location by a disturbance, it will tend to be pulled back to that location. However, when it's out of its equilibrium location, it pulls its neighbors out of their equilibrium locations too, and so on down the line. The result is that a transverse wave disturbance propagates through the material.

A transverse wave consists of:

  1. only crest

  2. only trough

  3. both crest and trough

  4. rarefaction and compressions


Correct Option: C
Explanation:

A transverse wave travels through a medium in the form of crests and troughs.

Hence it consists of both crests and troughs
Option C is the right answer

For propagation of a mechanical wave, the medium must possess

  1. inertia

  2. conductivity

  3. plasticity

  4. elasticity


Correct Option: A,D
Explanation:
  • MEDIUM SHOULD BE ISOTROPIC: The properties of the medium should be the same in all directions.
  • ELASTICITY : The medium should have elasticity so that the particles return back to their original positions after being displaced.
  • INERTIA : This allows the particles to store kinetic energy.
  • MINIMUM FRICTION : So that the particles oscillate and the wave travels for a sufficiently long time and distance.
  • these were the properties required for propagation of mechanical waves , so the answer is A and D.

Waves can undergo

  1. reflection

  2. refraction

  3. diffraction

  4. All of the above 


Correct Option: D
Explanation:

waves can go reflection , refraction and diffraction  like  light being an EM wave performs all these phenomenons.

so the answer is D.

Water waves are an example of waves that involve

  1. longitudinal motions.

  2. transverse motions.

  3. a combination of both longitudinal and transverse motions

  4. some unknown type of motions,


Correct Option: C
Explanation:

Water waves are an example of waves that involve a combination of both longitudinal and transverse motions. As a wave travels through the waver, the particles travel in clockwise circles. The radius of the circles decreases as the depth into the water increases.

so the answer is C.

Which of the following waves do not require any kind of medium to propagate ?

  1. Sound waves

  2. Earthquake

  3. Light Waves

  4. Water surface waves


Correct Option: C
Explanation:

electromagnetic waves donot require medium for propagation . light is a EM wave.

so the answer is C.

State whether true or false :
With the change of medium, the frequency doesn't change, however both the velocity and wavelength change 

  1. True

  2. False


Correct Option: A
Explanation:

with change in medium the wavelength and velocity of wave both are changed but being property of source remains constant and doesnot change.

so the answer is A

With propagation of longitudinal waves through a medium, the quantity transmitted is : 

  1. matter

  2. energy

  3. energy and matter

  4. energy, matter and momentum


Correct Option: B
Explanation:

longitudinal waves are propagated by  propagation of energy by particles of the medium.

so the answer is B.

When a wave is reflected from a ___________ medium, there is a phase change of $\pi$.

  1. rarer

  2. denser

  3. both

  4. none of the above


Correct Option: B
Explanation:

when reflection of wave takes place from the denser medium then  it undergoes a phase change of $\pi$ . 

answer is B.

State true or false :
Mechanical Waves are waves which propagate through a material medium.

  1. True

  2. False


Correct Option: A
Explanation:

mechanical waves  are waves which needs medium for propogation.. energy is transferred  while propagation from particle to particle of medium.

so the answer is A

Which of the following statements are true for wave motion ?

  1. Mechanical transverse waves can propagate through all mediums

  2. Longitudinal waves can propagate through solids only

  3. Mechanical transverse waves can propagate through solids only

  4. Longitudinal waves can propagate through vacuum


Correct Option: C
Explanation:

$1.$ Mechanical transverse waves cannot propagate through all the medium. They can only propagate through solids not in gas or a liquid because there is no mechanism for driving motion perpendicular to the propagation of the wave.

$2.$ Longitudinal wave can propagate through all type of medium.
$3.$ Mechanical transverse wave can propagate through solids only.
$4.$ Longitudinal wave cannot propagate through vaccum.
Hence, option $C$ is correct.

A man sets his watch by the noon whistle of a factory at a distance of $1.5 km.$ Then the number of seconds his watch slower than the clock of the factory (velocity of sound $= 332 m/s$) is 

  1. $4.52 sec$

  2. $5.35 sec$

  3. $2.18 sec$

  4. $3.76 sec$


Correct Option: A
Explanation:

time taken for the whistle to reach the person is $\dfrac{d}{v}$
$=\dfrac{1.5\times 1000}{332}=4.52sec$
$\therefore$ delay of his clock is $4.52s$

When a wave is reflected from a ___________ medium, there is no change of phase.

  1. rarer

  2. denser

  3. both

  4. none of the above


Correct Option: A
Explanation:

when reflection of wave takes place from the denser medium then  it undergoes a phase change of $\pi$ . Since, here in question the phase is not changing so the medium must be rarer.

answer is A.

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