Finding propagation speed/wavelength from an equation

[hopelessphysics]

Homework Statement

A wave is described by y=12sin(4t-8x). What is its propagation speed?
A. 0.2
B. 0.5
C. 4
D. 8
E. 12

Homework Equations

v=wavelength/period
v=wavelength×frequency

The Attempt at a Solution

period= 2π/w=2π/8=.7853
But confused on how to find the wavelength?

 

[marcusl]

No, that's incorrect. The definition of period is that that time after which the function y(t,x) takes on the same value, for a fixed location. If we fix the position (take x=0 for convenience), and start at t=0, at what time tp is y(tp,0) = y(0,0)? tp is the period.

Then you can fix the time and do the same for position to find the wavelength.

 

[hopelessphysics]

I'm sorry but I am not following what you are saying...could you re-explain it?

 

[marcusl]

Your wave is sinusoidal so it repeats whenever the argument increases by 2*pi. The period represents a 2*pi increase in time with the position held constant, while the wavelength represents a 2*pi increase in position while the time is held constant. These two conditions allow you to find the period and wavelength.