Understanding Traverse Wave Properties: Homework Questions

In summary, a 0.45 kg horizontal rope is fixed at its two ends and oscillates in the fundamental mode at a frequency of 4.0 Hz. The amplitude of the motion at the point x = 2.5 m is 0.199 m. The wave speed in the rope is 10 m/s and the tension is 18 N. The speed, amplitude, and tension were found using various equations and the given information.
  • #1
GGD
3
0

Homework Statement



In a demonstration, a 0.45 kg horizontal rope is fi xed in place at its two ends (x = 0 and x = 5.0 m) and made to oscillate up and down in the fundamental mode, at frequency 4.0 Hz. At t = 0, the point at x = 2.5 m has zero displacement and is moving upward in the positive direction of a y-axis with a transverse velocity of 5.0 m/s.

(a) What is the amplitude of the motion of that point?
(b) What is the wave speed in the rope?
(c) What is the tension in the rope?


Homework Equations



w=2*pi*f
k=2*pi*λ
y(x,y)=Asin(wt-kx)
v=sqrt(T/μ)
v=λ*f

The Attempt at a Solution



I already found to amplitude to be .199 m by taking the derivite of the wave equation and solving for A.

For part B, though the wave speed would simply be wavelength*frequency, but 20m/s is not the correct answer. I tried to mess around with a few other equations but they led me nowhere.

And for part C I know T is simply (v^2)*μ, but I obviously need to first find velocity.

Any help would be grealty appreciated, thanks!
 
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  • #2
What value did you use for the wavelength. The vibration is the fundamental which means the string is half a wavelength long .
 
  • #3
Alright so the speed should equal ((wavelength*freq)/2), or (5*4)/2 , which is equal to 10 m/s? That answer doesn't work for me either.
 
  • #4
First of all : you know the frequency is 4Hz and the wavelength is (2 x 5) =10m... this gives you the speed (v = fλ)
Speed = sqrt (T/μ) ...you should be able to get T ?
The amplitude is given by a SHM equation. Max velocity in SHM = ωA = 2∏fA
The midpoint of the string is doing SHM with max amplitude...
Hope this helps you to finish it.
 
  • #5
Alrigh I finally got it, I was dividing by 2 instead of multiplying by it. Thanks for your help!
 
  • #6
Great... well done
 

1. What is a traverse wave on a string?

A traverse wave on a string is a type of mechanical wave that travels along a medium, such as a string, in a perpendicular direction to the wave's motion. This means that the particles of the medium vibrate up and down as the wave passes through, creating a series of crests and troughs.

2. How is the speed of a traverse wave on a string determined?

The speed of a traverse wave on a string is determined by the tension of the string and the mass per unit length of the string. This is described by the equation v = √(T/μ), where v is the speed, T is the tension, and μ is the mass per unit length.

3. Can traverse waves on a string be reflected?

Yes, traverse waves on a string can be reflected when they encounter a boundary, such as the end of the string or a different type of medium. The angle of reflection will be equal to the angle of incidence, and the wave will continue to travel in the opposite direction.

4. What is the difference between a traverse wave and a longitudinal wave?

A traverse wave on a string is a type of transverse wave, which means that the particles of the medium vibrate perpendicular to the direction of the wave's motion. In contrast, a longitudinal wave has particles that vibrate parallel to the direction of the wave's motion. Sound waves, for example, are longitudinal waves.

5. How does the amplitude of a traverse wave on a string affect its energy?

The amplitude of a traverse wave on a string is directly proportional to its energy. This means that as the amplitude increases, the energy of the wave also increases. This can be seen in the larger vibrations and higher crests and troughs of a wave with a larger amplitude.

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