A wave is represented by the equation
`y = A sin(10pix + 15pit + (pi)/(3))`
where `x` is in meter and `t` is in seconds. The expression represents :

Options

A. (a) a wave travelling in the positive x-direction with a velocity `1.5 m//s`.
B. (b) a wave travelling in the negative x-direction with a velocity `1.5 m//s`.
C. ( c ) a wave travelling in the negative x-direction having a wavelength `0.2 m`.
D. ( cd) a wave travelling in the positive x-direction having a wavelength `0.2 m`.

Answer

B, C

Explanation

(b,c) `y = A sin (10pix + 15pit + pi//3)`
The standered equation of a wave travelling in `-X direction
is `y = A sin [(2pi)/(lambda)(vt + x) + (Phi)]`
rArr `y = A sin [(2piv)/(lambda)(t +(2pi)/(lambda) x + Phi]`
Comparing it with the given equation, we find
`(2piv)/(lambda) = 15pi` and (2pi)/(lambda) = 10pi`
rArr `lambda = (1)/(5) = 0.2m` and `v = (15pi)/(2pi)xx (1)/(5) = 1.5 m//s`