Transverse Wave: Amplitude, Wavelength, Speed & Direction

In summary, the transverse displacement of an harmonic wave on a stretched rope is y = 0.04 cos(2.5x-5t), where x and y are in meters and t is in seconds. The amplitude of this wave is A = m * 0.04 = 0.08 meters, the wavelength is l = 0.144 meters, the speed with which this wave travels is v = (wavelength* frequency) = (0.144*2.51) meters per second, and the direction of this wave is +x.
  • #1
mattmannmf
172
0
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 can't plot it to figure out the wave length.. any ideas?
 
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  • #2
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.
 
  • #3
so my new equation would be:
y=.04cos(2.5x) ? i get the wavelength to be 144 (just by graphing it) which is wrong
 
  • #4
mattmannmf said:
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.
 
  • #5
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?
 
  • #6
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 :)
 
  • #7
ahhh ok..wow that made everything clear..thanks
 

1. What is a transverse wave?

A transverse wave is a type of wave in which the particles of the medium move perpendicular to the direction of energy propagation. This means that the particles move up and down or side to side, rather than back and forth.

2. What is amplitude in a transverse wave?

Amplitude is the measure of the maximum displacement of particles from their rest position in a wave. In transverse waves, it refers to the maximum height of the wave crest or the depth of the wave trough.

3. What is wavelength in a transverse wave?

Wavelength is the distance between two consecutive points in a transverse wave that are in the same position in the wave cycle. This can be measured from crest to crest or from trough to trough.

4. How is speed calculated in a transverse wave?

The speed of a transverse wave is calculated by multiplying the wavelength by the frequency of the wave. This is because the frequency determines how many wave cycles occur in a given time period, and the wavelength is the distance traveled in one cycle.

5. Can a transverse wave change direction?

Yes, a transverse wave can change direction when it encounters a change in medium or when it is reflected off a surface. This is known as refraction and reflection, respectively.

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