Transverse Wave: Amplitude, Wavelength, Speed & Direction

[mattmannmf]

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 because it has 3 variables in stead of 2 so i can't plot it to figure out the wave length.. any ideas?

 

[Redbelly98]

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.

 

[mattmannmf]

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]

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.

 

[mattmannmf]

ahh ok...2.51.

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

 

[theneedtoknow]

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 traveling in the positive x direction and d(x,t) = Acos (kx+wt) for a wave traveling 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 traveling wave, and you should be able to solve for everything you need :)

 

[mattmannmf]

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