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Question

the equation of a progressive wave is given by y=5 sin (100πt0.4πx) 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/sWhich of the following statement are correct?

A
(1), (2) and (3)
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B
(2) and (3)
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C
(1) and (4)
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D
All are correct
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Solution

The correct option is D All are correct
the equation of a given progressive wave is
y=5sin(100πt0.4πx) ......(i)
The standard equation of a progressive wave is
y=asin(ωtKx) ...(ii)
Comparing (i) and (ii), we get
a=5m,ω=100π rad s1,k=o.4πm1
(1) Amplitude of the wave, a=5m
(2) Wavelength of the wave, λ=2πk=2π0.4π=5m
(3)Frequency of the wave, υ=ω2π=100π2π=50Hz
(4) Velocity of the wave, ν=υλ=(50s1)(5m)
=250ms1

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