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

Answer

B, C

Explanation

`y=A sin(10 pi x = 15 pi t + pi//3)`
The standard equation of a wave travelling in X-direction is
`y=A sin[(2pi)/(lamda)(vt+x)+(phi)]`
`rArry=A sin[(2pi v)/(lamda)t+(2pi)/(lamda)x+ phi]`
Comparing it with the given equation we find
`(2 pi v)/(lamda) = 15 pi`
and `(2 pi)/(lamda) = 10 pi`
`lamda = (1)/(5) = 0.2 m`
`:. v = (15 pi)/(2 pi) xx (1)/(5) = 1.5 m//s`.