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

The function f x = sin π x n ! − cos π x n + 1 ! is

periodic, with period 2 n + 1 !

MEDIUM

Earn 100

Displacement of two particles moving along $x -$ axis is given by-

$x_{1} = (8 + 3 s i n ω t) m$ and $x_{2} = (4 c o s ω t) m$
(where $ω = π rad \sec^{- 1})$

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Important Questions on Wave Motion on a String

EASY

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

EASY

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

In the wave equation

y = 0.5 \sin \frac{2 π}{λ} (400 t - x) m

the velocity of the wave will be :

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:

EASY

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

HARD

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

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

A travelling wave is described by the equation $y (x, t) = [0.05 \sin (8 x - 4 t)] m$ . The velocity of the wave is:

[All the quantities are in SI unit]

EASY

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

EASY

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

f : R \to R

is a function satisfying

f (2 x + 3) + f (2 x + 7) = 2 \forall x \in R

, then the period of

f (x)

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)

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

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

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>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

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

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

$y_{1} = a \sin (ω t - k x)$

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

MEDIUM

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

The function

f (x) = \sin (\frac{π x}{n!}) - \cos (\frac{π x}{(n + 1)!})

EASY

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

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

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_______

Displacement of two particles moving along x-axis is given by- x1=8 + 3 sin ωt m and x2=4 cos ωt m (where ω =π rad sec-1)

Important Questions on Wave Motion on a String

Learn and Prepare for any exam you want !

Displacement of two particles moving along $x -$ axis is given by-

$x_{1} = (8 + 3 s i n ω t) m$ and $x_{2} = (4 c o s ω t) m$
(where $ω = π rad \sec^{- 1})$