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The equation of a progressive wave is gi...

The equation of a progressive wave is given by y = 5 `sin(100pit - 0.4pix)` where y and x are in m and t is in s.
(1) The amplitude of the wave is 5 m.
(2) The wavelength of the wave is 5 m.
(3) The frequency of the wave is 50 Hz.
( 4) The velocity of the wave is 250 m `s^(-1)`
Which of the following statements are correct?

A

(I), (2) and (3)

B

(2) and (3)

C

(1) and (4)

D

All are correct

Text Solution

Verified by Experts

The correct Answer is:
D
The equation of a given progressive wave is `y=5 sin(100pit - 0.4pix)` …(i)
The standard equation of a progressive wave is
`y=a sin(omegat - kx)` ..(ii)
Comparing (i) and (ii), we get
`a=5 m, omega=100pi rad s^(-1), k = 0.47pi m^(-1)`
(1) Amplitude of the wave, a = 5 m
(2) Wavelength of the wave, `lamda=(2pi)/k=(2pi)/(0.4pi) =5 m`
(3) Frequency of the wave, `upsilon =(omega)/(3pi)=(100pi)/(2pi)=50 Hz`
(4) Velocity of the wave, v =`upsilonlamda = (50 s^(-1)) (5 m)`
`=250ms^(-1)`
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