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Two pulses in a stretched string, whose centres are initially $8 cm$ apart, are moving towards each other as shown in the figure. The speed of each pulse is $2 cm s^{- 1}$ . After $2 s$ the total energy of the pulses will be

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Important Questions on Waves

MEDIUM

Physics>Oscillations and Waves>Waves>Principle of Superposition of Waves

The sources of sound

A

and

B

produce a wave of

350 Hz

in same phase. A particle

P

is vibrating under an influence of these two waves. If the amplitudes at

P

produced by the two waves is

0.3 mm

and

0.4 mm

, the resultant amplitude of the point

P

will be, when

A P - B P = 25 cm

and the velocity of sound is

350 m s^{- 1}

EASY

Physics>Oscillations and Waves>Waves>Principle of Superposition of Waves

Two waves of the same kind and of the same amplitude

A

superpose at a point with a phase difference of

φ

between them. Find the resultant amplitude (R).

MEDIUM

Physics>Oscillations and Waves>Waves>Principle of Superposition of Waves

Two waves are simultaneously passing through a string and their equations are :

y_{1} = A_{1} \sin k (x - v t), y_{2} = A_{2} \sin k (x - v t + x_{0}) .

Given amplitudes

A_{1} = 12 mm

and

A_{2} = 5 mm

x_{0} = 3.5 cm

and wave number

k = 6.28 {cm}^{- 1} .

The amplitude of resulting wave will be _____

mm .

EASY

Physics>Oscillations and Waves>Waves>Principle of Superposition of Waves

The equations of two waves are given by :

$y_{1} = 5 \sin 2 π (x - v t) cm$

$y_{2} = 3 \sin 2 π (x - v t + 1.5) cm$

These waves are simultaneously passing through a string. The amplitude of the resulting wave is :

EASY

Physics>Oscillations and Waves>Waves>Principle of Superposition of Waves

Two harmonic travelling waves are described by the equations

y_{1} = a \sin (k x - ω t)

and

y_{2} = a \sin (- k x + ω t + ϕ)

The amplitude of the superposed wave is

HARD

Physics>Oscillations and Waves>Waves>Principle of Superposition of Waves

The interference pattern is obtained with two coherent light sources of intensity ratio

4 : 1

. And the ratio

\frac{I_{\max} + I_{\min}}{I_{\max} - I_{\min}}

\frac{5}{x}

. Then, the value of

x

will be equal to :

MEDIUM

Physics>Oscillations and Waves>Waves>Principle of Superposition of Waves

Two simple harmonic motions are represented by the equations

x_{1} = 5 \sin (2 π t + \frac{π}{4})

and

x_{2} = 5 \sqrt{2} (\sin 2 π t + \cos 2 π t) .

The amplitude of the second motion is _____ times the amplitude in the first motion.

HARD

Physics>Oscillations and Waves>Waves>Principle of Superposition of Waves

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

M N

and moves towards

Q

constantly at

60 km h^{- 1}

along the perpendicular bisector of

M N

. It crosses

Q

and eventually reaches a point

R

1800 m

away from

Q

. Let

ν (t)

represent the beat frequency measured by a person sitting in the car at time

t

. Let

ν_{p}, ν_{Q} and ν_{R}

be the beat frequencies measured at locations

P, Q

and

R

, respectively. The speed of sound in air is

330 m s^{- 1} .

Which of the following statement(s) is (are) true regarding the sound heard by the person?

EASY

Physics>Oscillations and Waves>Waves>Principle of Superposition of Waves

Two identical progressive waves moving in opposite direction superimpose to produce a stationary wave. The wavelength of each progressive wave is

λ

. The wavelength of the stationary wave is

EASY

Physics>Oscillations and Waves>Waves>Principle of Superposition of Waves

The amplitude and frequency of two waves is same which are from two different sources, overlap at a point. The ratio of intensity when two waves arrive

(\frac{π}{2})

out of phase to when they arrive in phase is

EASY

Physics>Oscillations and Waves>Waves>Principle of Superposition of Waves

A body is suspended from a string of length

1 m

and mass

2 g

. The mass of the body to produce a fundamental mode of

100 Hz

frequency in the string is
(Acceleration due to gravity

= 10 m s^{- 2}

)

MEDIUM

Physics>Oscillations and Waves>Waves>Principle of Superposition of Waves

If two waves of the same frequency and amplitude respectively on superposition produce a resultant disturbance of the same amplitude, the waves differ in phase by

EASY

Physics>Oscillations and Waves>Waves>Principle of Superposition of Waves

Two waves executing simple harmonic motion travelling in the same direction with same amplitude and frequency are superimposed. The resultant amplitude is equal to the

\sqrt{3}

times of amplitude of individual motions. The phase difference between the two motions is _____ (degree)

EASY

Physics>Oscillations and Waves>Waves>Principle of Superposition of Waves

Two light beams of intensities in the ratio of

9 : 4

are allowed to interfere. The ratio of the intensity of maxima and minima will be :

EASY

Physics>Oscillations and Waves>Waves>Principle of Superposition of Waves

Two simple harmonic waves having equal amplitudes of

8 cm

and equal frequency of

10 Hz

are moving along the same direction. The resultant amplitude is also

8 cm

. The phase difference between the individual waves is _____ degree.

MEDIUM

Physics>Oscillations and Waves>Waves>Principle of Superposition of Waves

A transverse wave along a stretched string has a speed of

30 m s^{- 1}

and a frequency of

250 Hz

. The phase difference between two points on the string,

10 cm

apart, at the same instant is

EASY

Physics>Oscillations and Waves>Waves>Principle of Superposition of Waves

A simple harmonic progressive wave is represented as

y = 0.03 s i n π (2 t - 0.01 x) m

. At a given instant of time, the phase difference between two particles

25 m

apart is

MEDIUM

Physics>Oscillations and Waves>Waves>Principle of Superposition of Waves

Three sinusoidal waves with the same angular frequency but with different amplitudes

A, \frac{A}{2}, \frac{A}{3}

and phase angles

0, \frac{π}{2}

and

π

respectively move along the same direction and superpose with each other. The amplitude of the resultant wave is given by

MEDIUM

Physics>Oscillations and Waves>Waves>Principle of Superposition of Waves

Three harmonic waves having equal frequency

v

and same intensity

I_{0}

, have phase angles

0, \frac{π}{4}

and

- \frac{π}{4}

respectively. When they are superimposed the intensity of the resultant wave is close to:

MEDIUM

Physics>Oscillations and Waves>Waves>Principle of Superposition of Waves

The displacement

y

of a particle, if given by

y = 4 \cos^{2} (\frac{t}{2}) \sin (1000 t) .

This expression may be considered to be a result of the superposition of how many simple harmonic motions?

Two pulses in a stretched string, whose centres are initially 8 cm apart, are moving towards each other as shown in the figure. The speed of each pulse is 2 cm s-1. After 2 s the total energy of the pulses will be

Important Questions on Waves

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Two pulses in a stretched string, whose centres are initially $8 cm$ apart, are moving towards each other as shown in the figure. The speed of each pulse is $2 cm s^{- 1}$ . After $2 s$ the total energy of the pulses will be