Question

The equation y=5 sin(3x-4), where y is in mm, x is in m and t is in secs, represents a wave motion. Determine the frequency, period and speed of the wave

Answer 1

You mean:
y = 5 sin (3x - 4 t)
without t, no wave

now lets look when t = 0
y = 5 sin 3x
y = 0 when x = 0
but this starts over when
3x = 2 pi
so
when x = (2/3) pi, new period
so
Wavelength = L = 2 pi/3

Now look at x = 0, how long for a period
t = 0 --> 0
4t = 2pi is a new one
so
t = pi/2 is a period

and of course
frequency = 1/period :)

Now if you divide wavelength by period you get speed
speed = distance/time
= [2 pi/3] / [pi/2] = (4/3) meter/sec

Answer 2

Solve