Question

The equation of a standing wave is `y=0.2`
`sinfrac{2pi}{0.3}xcdot cos frac{2pit}{0.01}` where x and y are in metres and t
is in seconds. The velocity of propagation of the wave
is
A. 30 `ms^(-1)`
B. 40 `ms^(-1)`
C. 300 `ms^(-1)`
D. 400 `ms^(-1)`

Answer 1

Correct Answer - a
The given wave equation is
`Y=0.2 sin frac(2pi)(0.3)xcos frac(2pit)(0.01)` ...(i)
Comparing Eq. (i) with standard wave equation
`y=a sin kx cos omega t,` we get
`omega = (2pi)/(0.01) rads^(-1) rArr k = (2k)/(0.3)rad//m`
`rArr` Wave velocity `omega/k=(2pi//0.01)/(2pi//0.3)=(0.3)/(0.01)=30 ms^(-1)`