# Transverse waves

The transverse displacement of an harmonic wave on a stretched rope is y = 0.04 cos(2.5 x - 5 t), where x and y are in meters and t is in seconds.

a) What is the amplitude of this wave?
A = m *
.04 OK

b) What is the wavelength of this wave?

c) What is the speed with which this wave travels?

d) In what direction is this wave propagating?
+x

e) What is the frequency (NOT the angular frequency) of this wave?
f = s-1

First off i need to find the wavelength. i am not sure where to start. in terms of the equation they gave me, idk how i can use that becuase it has 3 variables in stead of 2 so i cant plot it to figure out the wave length.. any ideas?

## Answers and Replies

Redbelly98
Staff Emeritus
Science Advisor
Homework Helper
To get wavelength, fix t to be any constant ... use t=0 for convenience.

You now have a periodic function in x, and the "period" of that function will be the wavelength.

so my new equation would be:
y=.04cos(2.5x) ? i get the wavelength to be 144 (just by graphing it) which is wrong

Redbelly98
Staff Emeritus
Science Advisor
Homework Helper
so my new equation would be:
y=.04cos(2.5x) ?
Yes, good.

i get the wavelength to be 144 (just by graphing it) which is wrong
No. Try using radians, not degrees.

ahh ok...2.51.

now im kind of stuck as in velocity... no idea how to get it. equation is
v=(wavelength* frequency)
how do i determine frequency?

These questions are most easily approached through the pure mathematical formula of waves

The wave equation is
D(x, t) = Acos(kx-wt) for a wave travelling in the positive x direction and d(x,t) = Acos (kx+wt) for a wave travelling in the negative x direction

k is something called the wave number and is equal to 2Pi/wavelength, and w is called the angular frequency and is equal to 2pi*frequency. These are the mathematics of transverse waves.

Look at your equation of the travelling wave, and you should be able to solve for everything you need :)

ahhh ok..wow that made everything clear..thanks