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

EASY

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Two progressive wave are said to be in opposite phase or out of phase if phase difference becomes $180^{o} = π$

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Important Questions on Waves

MEDIUM

Physics>Oscillations and Waves>Waves>Equation of a Progressive 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?

HARD

Physics>Oscillations and Waves>Waves>Equation of a Progressive 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})

EASY

Physics>Oscillations and Waves>Waves>Equation of a Progressive 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>Waves>Equation of a Progressive 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>Waves>Equation of a Progressive Wave

The distance between two points differing in phase by

60 °

on a wave having wave velocity

360 m s^{- 1}

and frequency

500 Hz

MEDIUM

Physics>Oscillations and Waves>Waves>Equation of a Progressive Wave

A transverse wave is represented by :

y = \frac{10}{π} sin (\frac{2 π}{T} t - \frac{2 π}{λ} x)

For what value of the wavelength the wave velocity is twice the maximum particle velocity?

EASY

Physics>Oscillations and Waves>Waves>Equation of a Progressive Wave

Consider a wire with density

(d)

and stress

(σ) .

For the same density, if the stress increases

2

times, the speed of the transverse waves along the wire changes by

HARD

Physics>Oscillations and Waves>Waves>Equation of a Progressive Wave

A particle of mass

\frac{2}{3} kg

with velocity

v = - 15 m s^{- 1}

t = - 2 s

is acted upon by a force

F = k - β t^{2}

. Here,

k = 8 N

and

β = 2 N s^{- 2}

. The motion is one-dimensional. Then, the speed at which the particle acceleration is zero again, is

EASY

Physics>Oscillations and Waves>Waves>Equation of a Progressive Wave

Two waves are represented by:

x_{1} = A \sin (ω t + \frac{π}{6})

and

x_{2} = A \cos ω t

. Then the phase difference between them is

MEDIUM

Physics>Oscillations and Waves>Waves>Equation of a Progressive 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:

MEDIUM

Physics>Oscillations and Waves>Waves>Equation of a Progressive Wave

A travelling wave in a medium is given by the equation

y = asin (ωt - kx)

. The maximum acceleration of the particle in the medium is

MEDIUM

Physics>Oscillations and Waves>Waves>Equation of a Progressive Wave

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

MEDIUM

Physics>Oscillations and Waves>Waves>Equation of a Progressive 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:

EASY

Physics>Oscillations and Waves>Waves>Equation of a Progressive Wave

The displacement of a wave is represented by

y = 0.6 \times 10^{- 3} \sin (500 t - 0.05 x),

where all the quantities are in their proper units. The maximum particle velocity

(i n m s^{- 1})

of the medium is

EASY

Physics>Oscillations and Waves>Waves>Equation of a Progressive Wave

Let $f (x) = \sin x + \cos a x$ be a periodic function. Then,

EASY

Physics>Oscillations and Waves>Waves>Equation of a Progressive 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?

HARD

Physics>Oscillations and Waves>Waves>Equation of a Progressive Wave

a, b

be two fixed positive integers such that

f (a + x) = b + {[b^{3} + 1 - 3 b^{2} f (x) + 3 b {\{f (x)\}}^{2} - {\{f (x)\}}^{3}]}^{1 / 3}

for all real

x

then

f (x)

is a periodic function with period

HARD

Physics>Oscillations and Waves>Waves>Equation of a Progressive 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>Waves>Equation of a Progressive Wave

The phase difference between the following two waves $y_{2}$ and $y_{1}$ is:

$y_{1} = a \sin (ω t - k x)$

$y_{2} = b \cos (ω t - k x + \frac{π}{3})$

EASY

Physics>Oscillations and Waves>Waves>Equation of a Progressive Wave

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

Two progressive wave are said to be in opposite phase or out of phase if phase difference becomes 180o=π

Important Questions on Waves

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Two progressive wave are said to be in opposite phase or out of phase if phase difference becomes $180^{o} = π$