`y=3 sin pi (t/2-x/4)` represents an equation of a prgressive wave, where t is in second and x is in metre. The distance travelled by the wave in 5 seconds is

Options

A. 8m
B. 10m
C. 5m
D. 32m

Answer

B

Explanation

The given equation of a progressive wave is `y=3 sin pi(t/2-x/4)=3sin 2 pi (t/4-x/8)`…………I
The standard equation of a progressive wave is
`y=y_(0)sin2pi(t/T-x/(lamda))` …………………. Ii
comparing I and ii we get
`T=4s, lamda=8m`
Velocity of wave `v=(lamda)/T=8/4=2ms^(-1)`
Distance travelled by wave in time t is
`S=vt`
or `S=2xx5=10m` (As t=5s (given))