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Test: MCQs (One or More Correct Option): Waves | JEE Advanced - JEE MCQ


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25 Questions MCQ Test 35 Years Chapter wise Previous Year Solved Papers for JEE - Test: MCQs (One or More Correct Option): Waves | JEE Advanced

Test: MCQs (One or More Correct Option): Waves | JEE Advanced for JEE 2024 is part of 35 Years Chapter wise Previous Year Solved Papers for JEE preparation. The Test: MCQs (One or More Correct Option): Waves | JEE Advanced questions and answers have been prepared according to the JEE exam syllabus.The Test: MCQs (One or More Correct Option): Waves | JEE Advanced MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: MCQs (One or More Correct Option): Waves | JEE Advanced below.
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*Multiple options can be correct
Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 1

A wave equation which gives the displacement along the y-direction is given by y = 10–4 sin (60t + 2x) where x and y are in metres and t is time in seconds. This represents a wave

Detailed Solution for Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 1

y = 10–4 sin (60t + 2x)
Comparing the given equation with the standard wave equation travelling in negative x-direction
y = a sin (ωt + k x) we get amplitude a = 10–4m

*Multiple options can be correct
Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 2

A transver se wave is described by the equation  The maximum particle velocity is equal to four times the wave velocity if 

Detailed Solution for Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 2



Given that the maximum particle velocity is equal to four times the wave velocity (c = f × λ)

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*Multiple options can be correct
Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 3

An air column in a pipe, which is closed at one end, will be in resonance with a vibrating tuning fork of frequency 264 Hz if the length of the column in cm is :

Detailed Solution for Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 3

The wavelengths possible in an air column in a pipe which has one closed end is

n = 264 Hz as it is in resonance with a vibrating turning fork of frequency 264 Hz.

   

*Multiple options can be correct
Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 4

A tube, closed at one end and containing air, produces, when excited, the fundamental note of frequency 512 Hz. If the tube is open at both ends the fundamental frequency that can be excited is (in Hz)

Detailed Solution for Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 4



*Multiple options can be correct
Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 5

The displacement of particles in a string stretched in the x-direction is represented by y. Among the following expressions for y, those describing wave motion are :

Detailed Solution for Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 5

For wave motion , the differential equation is

     ....(i)

NOTE : The wave motion is characterized by the two conditions

*Multiple options can be correct
Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 6

An organ pipe P1 closed at one end vibrating in its first harmonic and another pipe P2 open at ends vibrating in its third harmonic are in resonance with a given tuning fork.
The ratio of the length of P1 to that of P2 is

Detailed Solution for Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 6


*Multiple options can be correct
Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 7

Velocity of sound in air is 320 m/s. A pipe closed at one end has a length of 1 m. Neglecting end corrections, the air column in the pipe can resonate for sound of frequency :

Detailed Solution for Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 7

*Multiple options can be correct
Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 8

A wave is represented by the equation

where x is in meters and t is in seconds. The expression represents :

Detailed Solution for Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 8

y = A sin (10 πx + 15 πt + π/3)

The standard equation of a wave travelling in – X direction

Comparing it with the given equation, we find

*Multiple options can be correct
Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 9

Two identical straight wires are stretched so as to produce 6 beats per second when vibrating simultaneously. On changing the tension slightly in one of them, the beat frequency remains unchanged. Denoting by T1 , T2 the higher and the lower initial tension in the strings, then it could be said that while making the above changes in tension,

Detailed Solution for Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 9


Initially beat frequency (f1 - f2) = 6.
The beat frequency remains unchanged which is possible when f2 increases and f1 decreases. Thus T2 increases and T1  decreases.

*Multiple options can be correct
Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 10

The displacement y of a particle executing periodic motion is given by 

This expression may be considereed to be a result of the superposition of

Detailed Solution for Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 10

= 2 [cos t + 1] sin 1000t
= 2 cos t sin 1000t + 2 sin 1000t
= sin 1000t + sin 999t + 2 sin 1000t

*Multiple options can be correct
Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 11

A sound wave of frequency f travels horizontally to the right. It is reflected from a large vertical plane surface moving to left with a speed v. The speed of sound in medium is C

Detailed Solution for Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 11

Frequency of reflected wave is f '' 

Wavelength of reflected wave 

*Multiple options can be correct
Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 12

A string of length 0.4 m and mass 10–2 kg is tightly clamped at its ends. The tension in the string is 1.6 N. Identical wave pulses are produced at one end at equal intervals of time, Δt. The minimum value of Δt which allows constructive interference between successive pulses is

Detailed Solution for Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 12

KEY CONCEPT : The time required for constructive interference  equal to the time period of a wave pulse.


*Multiple options can be correct
Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 13

The (x, y) co-ordinates of the corners of a square plate are (0, 0), (L, 0), (L, L) and (0, L). The edges of the plate are clamped and transverse standing waves are set up in it. If u(x, y) denotes the displacement of the plate at the point (x, y) at some instant of time, the possible expression(s) for u is (are)  (a = positive constant)

Detailed Solution for Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 13

Due to the clamping of the square plate at the edges, its displacements along the x and y axes will individually be zero at the edges. Only the choices (b) and (c) predict these displacements correctly. This is because sin 0 = 0.
Option (a) :


*Multiple options can be correct
Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 14

A transverse sinusoidal wave of amplitude a, wavelength l and frequency f is travelling on a stretched string. The maximum speed of any point on the string is v/10, where v is the speed of propagation of the wave. If a = 10–3m and v = 10 m s–1, then λ and f are given by

Detailed Solution for Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 14

NOTE : For a transverse sinusodial wave travelling on a string, the maximum velocity is aω.


*Multiple options can be correct
Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 15

y(x, t) = 0.8/[4x+5t)2+5] represents a moving pulse, where x and y are in meter and t in second. Then

Detailed Solution for Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 15

We know that equation of moving pulse is

y = f (x + vt)       ... (2)

On comparing (1)  and (2), we get

So, the wave will travel a distance of 2.5 m in 2 sec.

At

∴ maximum displacement is 0.16 m

The graph for the given equation is drawn. This is symmetric about y-axis.

*Multiple options can be correct
Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 16

In a wave motion y = a sin (kx - ωt), y can represent

Detailed Solution for Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 16

In the wave motion y = a (kx - ωt) , y can represent electric and magnetic fields in electromagnetic waves and displacement and pressure in sound waves.

*Multiple options can be correct
Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 17

Standing waves can be produced

Detailed Solution for Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 17

Standing waves are produced by two similar waves superposing while travelling in opposite direction.
This can happen in case (a), (b) and (c).

*Multiple options can be correct
Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 18

As a wave propagates,

Detailed Solution for Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 18

For a plane wave, intensity (energy crossing per unit area  per unit time) is constant at all points.
But for a spherical wave, intensity at a distance r from a point source of power (P), is given by 

But the total intensity of the spherical wave over the spherical surface centered at the source remains constant at all times.

NOTE :  For line source 

*Multiple options can be correct
Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 19

A student performed the experiment to measure the speed of sound in air using resonance air-column method. Two resonances in the air-column were obtained by lowering the water level. The resonance with the shorter air-column is the first resonance and that with the longer air-column is the second resonance. Then,

Detailed Solution for Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 19

At second resonance the length of air column is more as compared to first resonance. Now, longer the length of air column, more is the absorption of energy and lesser is the intensity of sound heard.

As shown in the figure, the length of the air column at the first resonance is somewhat shorter than 1/4 th of the wavelength of the sound in air due to end correction.

*Multiple options can be correct
Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 20

A person blows into open-end of a long pipe. As a result, a high pressure pulse of air travels down the pipe.
When this pulse reaches the other end of the pipe,

Detailed Solution for Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 20

When sound pulse is reflected through a rigid boundary (closed end of a pipe), no phase change occurs between the incident and reflected pulse i.e., a high pressure pulse is reflected as a high pressure pulse.
When a sound pulse is reflected from open end of a pipe, a phase change of a radian occurs between the incident and the reflected pulse. A high pressure pulse is reflected as a low pressure pulse.

*Multiple options can be correct
Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 21

A horizontal stretched string, fixed at two ends, is vibrating in its fifth harmonic according to the equation, y(x, t) = (0.01 m) sin [(62.8 m–1)x] cos[(628 s–1)t]. Assuming π = 3.14, the correct statement(s) is (are)

Detailed Solution for Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 21

y = [0.01 sin (62.8x)] cos (628 t).


The midpoint M is an antinode and has the maximum displacement = 0.01 m

The fundamental frequency = 

*Multiple options can be correct
Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 22

Two vehicles, each moving with speed u on the same horizontal straight road, are approaching each other. Wind blows along the road with velocity w. One of these vehicles blows a whistle of frequency f1. An observer in the other vehicle hears the frequency of the whistle to be f2. The speed of sound in still air is V. The correct statement(s) is (are)

Detailed Solution for Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 22


*Multiple options can be correct
Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 23

A student is performing an experiment using a resonance column and a tuning fork of frequency 244 s–1. He is told that the air in the tube has been replaced by another gas (assume that the column remains filled with the gas). If the minimum height at which resonance occurs is (0.350 ± 0.005) m, the gas in the tube is

(Useful information: 

 The molar masses M in grams are given in the options. Take the values of  for eachgas as given there.)

Detailed Solution for Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 23


For monatomic gas γ =1.67



∴ (d) is the correct option.
For diatomic gas γ = 1.4

∴ (b)  is incorrect

*Multiple options can be correct
Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 24

One end of a taut string of length 3 m along the x-axis is fixed at x = 0. The speed of the waves in the string is 100 ms–1. The other end of the string is vibrating in the y-direction so that stationary waves are set up in the string. The possible waveform (s) of these stationary waves is(are)

Detailed Solution for Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 24

Clearly in the given situation a displacement node is present at x = 0 and a displacement antinode is present at x = 3 m.
Therefore, y = 0 at x = 0 and y =±A at x = 3 m.

a, c and d are the correct options which satisfy the above conditions.

*Multiple options can be correct
Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 25

Two loudspeakers M and N are located 20 m apart and emit sound at frequencies 118 Hz and 121 Hz, respectively. A car is initially at a point P , 1800 m away from the midpoint Q of the line MN and moves towards Q constantly at 60 km/hr along the perpendicular bisector of MN. It crosses Q and eventually reaches a point R, 1800 m away from Q. Let v(t) represent the beat frequency measured by a person sitting in the car at time t. Let vP , vQ and vR be the beat frequencies measured at locations P, Q and R, respectively. The speed of sound in air is 330 ms–1. Which of the following statement(s) is(are) true regarding the sound heard by the person?

Detailed Solution for Test: MCQs (One or More Correct Option): Waves | JEE Advanced - Question 25




∴ nP + nR = 2 nQ ⇒ (A) is correct option
In general when the car is passing through A



i.e.,   α = 90° (at Q)
⇒ (b) is correct option.

  … (ii)

    …(iii)
From (ii) & (iii)


∴ (c) is the correct option

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