A wave pulse in a string is described by the equation y 1 = 5 3 x - 4 t 2 + 2 and another wave pulse in the same string is described by y 2 = - 5 3 x + 4 t - 6 2 + 2 . The values of y 1 , y 2 and x are in metres and t is in seconds. Which of the following statement is correct?

At x = 1 m , y 1 and y 2 always cancel

y 1 travels along - x -direction and y 2 along + x -direction

Both y 1 and y 2 travel along + x -direction

At time t = 1 s , y 1 and y 2 exactly cancel everywhere

At time t = 3 s , y 1 and y 2 exactly cancel everywhere

MEDIUM

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Two waves are passing through a region. They are represented by $y_{1} = (2.0 cm) \sin [(3.14 {cm}^{- 1}) x - (157 s^{- 1}) t]$ and $y_{2} = (2.5 cm) \sin [(1.57 {cm}^{- 1}) x - (314 s^{- 1}) t]$ . The magnitude of displacement of the particle at $x = 4.5 cm$ at time $t = 5.0 ms$ due to the presence of these two waves is $k \times 10^{- 2} cm$ . Find $|k|$ .

(Take $π = 3.14$ and $\sqrt{2} = 1.4$ )

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Important Questions on Wave Motion on a String

MEDIUM

Physics>Oscillations and Waves>Wave Motion on a String>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?

MEDIUM

Physics>Oscillations and Waves>Wave Motion on a String>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>Wave Motion on a String>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)

MEDIUM

Physics>Oscillations and Waves>Wave Motion on a String>Superposition of Waves

A wave pulse in a string is described by the equation

y_{1} = \frac{5}{{(3 x - 4 t)}^{2} + 2}

and another wave pulse in the same string is described by

y_{2} = \frac{- 5}{{(3 x + 4 t - 6)}^{2} + 2}

. The values of

y_{1}, y_{2}

and

x

are in metres and

t

is in seconds. Which of the following statement is correct?

EASY

Physics>Oscillations and Waves>Wave Motion on a String>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

HARD

Physics>Oscillations and Waves>Wave Motion on a String>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>Wave Motion on a String>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 :

HARD

Physics>Oscillations and Waves>Wave Motion on a String>Superposition of Waves

Two identical coherent sound sources $R$ and $S$ with frequency $f$ are $5 m$ apart. An observer standing equidistant from the source and at a perpendicular distance of $12 m$ from the line $R S$ hears maximum sound intensity.

When he moves parallel to $R S$ , the sound intensity varies and is a minimum when he comes directly in front of one of the two sources. Then, a possible value of $f$ is close to (the speed of sound is $330 m / s$ )

EASY

Physics>Oscillations and Waves>Wave Motion on a String>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

MEDIUM

Physics>Oscillations and Waves>Wave Motion on a String>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>Wave Motion on a String>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}

MEDIUM

Physics>Oscillations and Waves>Wave Motion on a String>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:

EASY

Physics>Oscillations and Waves>Wave Motion on a String>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>Wave Motion on a String>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}

)

HARD

Physics>Oscillations and Waves>Wave Motion on a String>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>Wave Motion on a String>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.

EASY

Physics>Oscillations and Waves>Wave Motion on a String>Superposition of Waves

Sound waves from a loudspeaker reach a point

P

via two paths which differ in length by

1.8 m

. When the frequency of sound is gradually increased, the resultant intensity at

P

is found to be maximum the frequency is

1000 Hz

. At what next higher frequency will a maximum be detected?
(velocity of sound

= 360 m / s)

EASY

Physics>Oscillations and Waves>Wave Motion on a String>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).

EASY

Physics>Oscillations and Waves>Wave Motion on a String>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

MEDIUM

Physics>Oscillations and Waves>Wave Motion on a String>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

Two waves are passing through a region. They are represented by y1=(2.0cm)sin3.14cm-1x-157s-1t and y2=(2.5cm)sin1.57cm-1x-314s-1t . The magnitude of displacement of the particle at x=4.5 cm at time t=5.0 ms due to the presence of these two waves is k×10-2 cm. Find k. (Take π=3.14 and2=1.4 )

Important Questions on Wave Motion on a String

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