In the wave equation, y = A sin 2 π a ( x - b t ) ,

the wavelength of wave is a b .

A transverse wave travelling on a stretched string is represented by the equation, y = 2 ( 2 x - 6 . 2 t ) 2 + 20 ; where x and y are in meter and t is in second , Then,

amplitude of the wave is 0 . 1 m .

frequency of the wave is 20 Hz .

wavelength of the wave is 1 m .

MEDIUM

Earn 100

Select the wrong statement about a progressive wave.

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Important Questions on Waves

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

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

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:

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_______

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})

MEDIUM

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

A wave travelling along the x-axis is described by the equation

y (x, t) = 0.005 \cos (α x - β t)

. If the wavelength and the time period of the wave are

0.08 m and 2.0 s

, respectively, than

α

and

β

in appropriate unit are

MEDIUM

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

A wave is represented by the equation

$y = (0.001 mm) \sin [(50 s^{- 1}) t + (2.0 m^{- 1}) x]$

MEDIUM

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

The equation of a transverse wave traveling along the positive

x -

axis with amplitude

0.2 m

, velocity

360 m s^{- 1}

and wavelength

60 m

be written as

MEDIUM

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

When a wave travels in a medium, the particle displacement is given by the equation

y = a \sin 2 π (b t - c x)

where a, b and c are constants. The maximum particle velocity will be twice the wave velocity if

EASY

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

Equation of a progressive wave is given by, $y = 0.2 \cos π (0.04 t + 0.02 x - \frac{π}{6})$ . The distance is expressed in $cm$ and time in second. The minimum distance between two particles having the phase difference of $π / 2$ is _____ $cm$ .

MEDIUM

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

In the wave equation,

y = A \sin \frac{2 π}{a} (x - b t)

HARD

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

y (x, t) = \frac{0.8}{{(4 x + 5 t)}^{2} + 5}

represents a moving pulse, where x and y are in metre and t in second. Then :

MEDIUM

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

A wave travelling along a string is described by the equation

y = a \sin (ω t - k x)

the maximum particle velocity is

MEDIUM

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

If the fundamental period of function

f (x) = s i n x + c o s (\sqrt{4 - a^{2}}) x

4 π

, then the value of

a

is/are:

MEDIUM

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

If the equation of transverse wave is

y = \sin (k x - 2 t)

, then the maximum particle velocity is

HARD

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

A sinusoidal wave is travelling on a string with speed

40 cm / s

. The displacement of the particles of the string at

x = 10 cm

varies with time according to

y = (5.0 cm) \sin [1.0 - (4.0 s^{- 1}) t]

. The linear density of the string is

4.0 g / cm

HARD

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

A transverse wave travelling on a stretched string is represented by the equation,

y = \frac{2}{(2 x - 6.2 t)^{2} + 20}

; where

x and y

are in

meter

and

t

is in

second

, Then,

EASY

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

The Period of

\sin^{2} θ

MEDIUM

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

A particle on the trough of a wave at any instant will come to the mean position after a time :
(T = time period)

EASY

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

The equation of a wave propagating in a medium is

y = a \sin k (x - v t)

,where y is the displacement of the particle in the medium at a distance x at any instant t. Which of the following statement (s) is/are true ?

Select the wrong statement about a progressive wave.

Important Questions on Waves

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