Question

the equation of a wave is given by y=v sin w(x/v-k pie) where w is angular velocity and v is linear velocity find the dimension of x and K

Answer 1

k is defined as wave number.
as it is inverse of wavelength.
.i.e
k = 2.pi/lamda
unit = > m^-1
therfore dimension for k is:
L^-1 M^0 T^0. a sin w [x/v -k]
M⁰L⁰T^-1(L¹/M⁰L¹T^-2)
K=M⁰L⁰T^-1/M⁰L⁰T^-2
K=T
X=1