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This mock test of Waves MCQ Level - 2 for IIT JAM helps you for every IIT JAM entrance exam.
This contains 10 Multiple Choice Questions for IIT JAM Waves MCQ Level - 2 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

When a source of sound of frequency crosses a stationary observer with a speed v, ( « speed of sound v), the apparent change in frequency Δf is given by :

Solution:

The correct answer is :

QUESTION: 2

In a stationary wave that forms as a result of reflection of wave from an obstacle the ratio of the amplitude at an antinode to the amplitude at node is n. The fraction of energy reflected is :

Solution:

Let a_{i}, and a_{r} be the amplitudes of incident and reflected waves. Then

∴ Fraction of energy reflected is

The correct answer is:

QUESTION: 3

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

The expression may be consider to be a result of the superposition of independent harmonic motions :

Solution:

The given equation can be written as

y = 2(cost + 1) sin(1000t)

= 2cost sin 1000t + 2sin(1000t)

= sin(1001t) + sin(999t) + 2sin(1000t)

i.e. the given expression is a small of superposition of three independent harmonic motions of angular frequencies 999,1000 and 1001 rad/sec.

The correct answer is: Three

QUESTION: 4

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 :

Solution:

Only first equation is the equation of standing wave. The condition for a function x and t to represent a wave is :

Only first equation satisfies the condition.

The correct answer is:

QUESTION: 5

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

Solution:

Wave velocity

Maximum particle velocity

Given,

or

The correct answer is:

QUESTION: 6

A transverse wave in metres, is propagating along +ve X- axis on a string. A light insect starts crawling on the string with the velocity of 5 cm/s at t = 0 along the +ve X- axis from a point where x = 5 cm . After 5 s the difference in the phase of its position is equal to :

Solution:

At t = 0, x = 5 cm, initial phase of insect

After 5s insect will more a distance s = vt = 25 cm

So, it will beat x = 30 cm .

At this instant,

The correct answer is:

QUESTION: 7

Speed of sound wave is v. If a reflector moves towards a stationary source emitting waves of frequency f with speed u, the wavelength of reflected wave will be :

Solution:

Apparent frequency for reflector (will act as an observer) would be :

where f = actual frequency of source.

After being reflected the apparent frequency will further change and the reflector will now behave as a source. The apparent frequency will now become :

Substituting value of f_{1}, we get

The correct answer is:

QUESTION: 8

A train is moving with a constant speed along a circular track. The engine o f the train emits a sound of frequency f. The frequency heard by the guard at rear end of the train :

Solution:

Let v be the speed of sound and u the speed of train.

Then

and

The correct answer is: is equal to f

QUESTION: 9

A standing wave is maintained in a homogeneous string of cross-sectional area a and density p. It is formed by superposition of two waves travelling in opposite directions given by the equation.

The total mechanical energy confined between the sections corresponding to the adjacent antinodes is :

Solution:

Distance between two adjacent antinodes is

Volume of string between two adjacent antinodes

Here, u is the energy density (energy per unit volume) which is equal to

The correct answer is :

QUESTION: 10

A travelling wave is partialy reflected partialy and partly transmitted from a rigid boundary. Let a_{v} a_{r} and a_{t} be the amplitudes of incident wave, reflected wave and transmitted wave and l_{i}, I_{r} and l_{t} be the corresponding intensities. Then choose the correct alternative:

Solution:

only when other properties like density of medium, speed of wave etc, remains the same

In incident and reflected waves medium is same. Therefore, other properties are same. Hence,

The correct answer is:

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