Home
Class 12
PHYSICS
An equation y = a cos ^( 2 ) (2 pi...

An equation ` y = a cos ^( 2 ) (2 pi nt - (2pi x ) / ( lamda ) ) ` represents a wave with : -

A

amplitude a, frequency n and wavelength ` lamda `

B

amplitude a, frequency 2n and wavelength 2`lamda `

C

amplitude ` (a ) /( 2 ) ` , frequency 2n and wavelength `lamda`

D

amplitude ` ( a ) / ( 2 ) `, frequency 2n and wavelength ` ( lamda ) / ( 2 ) `

Text Solution

Verified by Experts

The correct Answer is:
D
` y = a cos ^ 2 ( 2 pi nt - ( 2pi x ) /( lamda ) ) `
` = ( a ) /( 2 ) [ 1 + cos 2 ( 2pi nt - ( 2pi ) / ( lamda ) x ) ] `
` rArr y = ( a ) /( 2 ) [ 1 + cos 2pi { 2 nt - ( x ) / ( lamda //2 ) }] `
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

Show that the equation y=a sin (2pi nt-(2pi)/lambda x) respresents a progressive wave of velocity C given by C=n lambda .

A sound wave is travelling in a medium.If equation of displacement wave in the medium is given by y = 2cos ( 2 pi x - 100 pi t + pi/2 ) then equation of pressure waves will be (B rarr Bulk modulus of medium) (А) P = 4B pi sin ( 2 pi x - 100 pi t ) (В) P = 4B pi sin ( 2 pi x + 100 pi t ) (C) P = 4B pi cos ( 2 pi x - 100 pi t ) (D) P = 4B pi cos ( 2 pi x + 100 pi t )

Knowledge Check

  • The equation y=A cos^(2) (2pi nt -2 pi (x)/(lambda)) represents a wave with

    A
    Amplitude `A//2`, frequency `2n` and wavelength `(lamda)/(2)`
    B
    Amplitude `A//2` frequency `2 n` and wavelength `lamda`
    C
    Amplitude ` A` , frequency ` 2 n` and wavelength `2lamda`
    D
    Amplitude ` A` , frequency `n` and wavelength `lambda`

  • The equation of a progressive wave is y = A sin (omega t - (2pi x)/(lamda)) . In terms of frequency and velocity of the wave, this equation is written as:

    A
    `y = A sin 2pi n (t - (v)/(x))`
    B
    `y = A sin 2pi n (t - (x)/(v))`
    C
    `y = A sin 2pi (n t- (x)/(v))`
    D
    `y = 2A sin pi (nt = (x)/(v))`

  • A plane progressive wave is represented by the equation y= 0.25 cos (2 pi t - 2 pi x) The equation of a wave is with double the amplitude and half frequency but travelling in the opposite direction will be :-

    A
    `y = 0.5 cos (pi t - pi x)`
    B
    `y = 0.5 cos (2 pi t + 2 pi x)`
    C
    `y = 0.25 cos (pi t + 2 pi x)`
    D
    `y = 0.5 cos (pi t +pi x)`

    • Similar Questions

    Explore conceptually related problems

    The equation of a progressive wave is y = A sin (omega t - (2pi x)/(lamda)) This equations can be expressed in terms of wavelength and velocity of the wave as

    The equation of the stationary wave is y = 2 A sin (( 2 pi c t)/( lambda)) cos (( 2 pi x)/( lambda)) Which of the following statements is wrong?

    The equation of standing wave along a sonometer wire is given by y=2A cos ((2pi x)/(lambda)) sin omega t. This represent a standing wave having the origing as

    The equation vec(phi)(x,t)=vec(j)sin ((2pi)/(lambda)vt)cos ((2 pi)/(lambda)x) represents

    The equation y = a sin (2pi)/(lamda) (vt - x) is an expression for s

    Home
    Profile