Equation of progressive wave is y = a sin ⁡ 10 π x + 11 π t + π 3

It is travelling in the positive x - direction

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

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Equation of progressive wave is

$y = a \sin [10 π x + 11 π t + \frac{π}{3}]$

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Important Questions on Wave Motion on a String

MEDIUM

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

When a particle of mass

m

is attached to a vertical spring of spring constant

k

and released, its motion, is described by

y (t) = y_{0} \sin^{2} ωt

, where '

y

' is measured from the lower end of upstretched spring. Then

ω

is :

HARD

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

Two vectors

\vec{A}

and

\vec{B}

are defined as

\vec{A} = a \hat{i}

and

\vec{B} = a (\cos ω t \hat{i} + \sin ω t \hat{j})

, where a is a constant and

ω = \frac{π}{6} rad s^{- 1} .

|\vec{A} + \vec{B}| = \sqrt{3} |\vec{A} - \vec{B}|

at time

t = τ

for the first time, the value of

τ

in seconds, is_______

EASY

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

A uniform thin rope of length

12 m

and mass

6 kg

hangs vertically from a rigid support and a block of mass

2 kg

is attached to its free end. A transverse short wave train of wavelength

6 cm

is produced at the lower and the rope. What is the wavelength of the wave train (in

cm

) when it reaches the top of the rope?

EASY

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

An observer on the sea shore observes

54

waves reaching the coast per minute. If the wavelength is

10 m

, the velocity of the wave is

EASY

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

A travelling harmonic wave is represented by the equation

y (x, t) = 10^{- 3} \sin (50 t + 2 x),

where

x

and

y

are in meter and

t

is in seconds. Which of the following is a correct statement about the wave?

MEDIUM

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

A transverse wave propagating along $x$ -axis is represented by

$y (x, t) = 8.0 \sin (0.5 π x - 4 π t - \frac{π}{4})$

where $x$ is in meters and $t$ is in seconds. The speed of the wave is

EASY

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

A progressive wave travelling along the positive

x -

direction is represented by

y (x, t) = A s i n (k x - ω t + ϕ)

. Its snapshot at

t = 0

is given in the figure.
Question Image

For this wave, the phase

ϕ

is:

EASY

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

A wave is represented by the equation

y = (0.02 m) \sin (5 π x - 20 t) .

The minimum distance between the two particles always having the same speed is. (Assume

x

and

t

are in SI units)

MEDIUM

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

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>Equation of Wave

The maximum transverse velocity and maximum transverse acceleration of a harmonic wave in a

o n e - d i m e n s i o n a l

string are

1 m s^{- 1}

and

1 m s^{- 2}

respectively. The phase velocity of the wave is

1 m s^{- 1}

. The waveform is

EASY

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

Which of the following equations represents a travelling wave?

MEDIUM

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

A transverse wave of frequency

500 Hz

and speed

100 m s^{- 1}

is travelling in the positive,

x

direction on a long string. A time

t = 0 s

the displacements at

x = 0.0 m

and at

x = 0.25 m

are

0.0 m

and

0.02 m,

respectively. The displacement at

x = 0.2 m

t = 5 \times 10^{4} s

is,

EASY

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

A sound wave of frequency

245 Hz

travels with the speed of

300 {m s}^{- 1}

along the positive x-axis. Each point of the wave moves to and fro through a total distance of

6 cm

. What will be the mathematical expression of this travelling wave?

MEDIUM

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

For a transvers wave travelling, along a straight line, the distance between two peaks (crests) is

5 m

, while the distance between one crest and one trough is

1.5 m

. The possible wavelengths (in

m

) of the waves are:

MEDIUM

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

The transverse displacement at position $x$ and time $t$ in a string due to a travelling wave is given by $y (x, t) =$ $3.0 \cos (π x - 4 π t) cm$ , where $x$ is in centimeters and $t$ is in seconds. Which of the following statements is wrong?

Question Image

EASY

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

The equation of a wave is given by

y = 10 \sin ((\frac{2 π}{45}) t + α) .

If the displacement at

t = 0 s

5 cm,

then the total phase at

t = 7.5 s

EASY

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

The propagation constant or angular wave number is

EASY

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

A uniform string of length $20 m$ is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the support is

(Take, $g = 10 m s^{- 2}$ )

HARD

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

A particle performing S.H.M. starts from the equilibrium position and its time period is

16 s

. After

2 s

its velocity is

π m s^{- 1} .

Amplitude of oscillation is

(\cos 45^{o} = \frac{1}{\sqrt 2})

MEDIUM

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

A simple harmonic motion is represented by:

y = 5 (\sin 3 π t + \sqrt{3} \cos 3 π t) cm

The amplitude and time period of the motion are:

Equation of progressive wave is y=asin⁡10πx+11πt+π3

Important Questions on Wave Motion on a String

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Equation of progressive wave is

$y = a \sin [10 π x + 11 π t + \frac{π}{3}]$