The motion of a vibrating system is described by the function y(x, t) = A0e^(-at)sin(kx-ωt). If t refers to time in seconds and x refers to distance in meters, what must the units of k be?

Question

1/s
s
1/m
unitless
m/s
m

Answer 1

k x must be the same units as ω t which is 2 pi f t which is 2 pi t/T which is no units (angle) so
k x must be no units so k must be 1/meter

by the way if L is wavelength and T is period
sin(kx-ωt) is the same as sin (2 pi x/L - 2 pi t/T)
so kx has same units as x/L so k has same units as 1/wavelength