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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)/(2)` and frequency n

B

amplitude A and frequency 2n

C

amplitude `(A)/(2)` and frequency 2n

D

amplitude A and frequency n

Text Solution

Verified by Experts

The correct Answer is:
C
The equation `y = A cos^(2) (2pi nt - (2pi x)/(lamda))` is written in the standard form by using
`cos^(2) theta = (1 + cos 2 theta)/(2)`
`:. y = A [(1 + cos 2 (2pi nt - (2pi x)/(lamda)))/(2)]`
`y = (A)/(2) cos (4pi nt - (4pi x)/(lamda)) + (A)/(2)`
Comparing with the standard equation
`y = A cos (omega t - Kx)`
We get the amplitude `(A)/(2) and omega = 4pin`
`:.` Frequency `= (omega)/(2pi) = (4pi n)/(2pi) = 2n`
`:.` It represents a wave of amplitude `(A)/(2)` and frequency 2n
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