Amplitude of velocity (Travelling wave)

In summary, the given wave traveling along a long string has the form y(x,t) = 20sin(3x-2t), where x is in metres and t is in seconds. To find the amplitude of the velocity of any particle on the string, the partial derivative of y with respect to t is taken, resulting in -40cos(3x-2t). The amplitude of the velocity is then determined to be -40 m/s or 40 m/s depending on whether the absolute value is taken.
  • #1
Alex_Neof
41
2

Homework Statement


A wave traveling along a long string has the form:

##y(x,t) = 20sin(3x - 2t),

## where ##x## is in metres and ##t## is in seconds.

Find the amplitude of the velocity of any particle of the string.

2. Homework Equations

Do I just find ##\frac {\partial y}{\partial t} ## ?

The Attempt at a Solution



So ##\frac {\partial y}{\partial t} = -40cos(3x - 2t) ##, therefore the amplitude of the velocity of any particle of the string is ##-40 m/s##. Absolute value ##40 m/s##.
Or is it more involved?
 
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  • #2
Your work looks good to me. However, the units for y are not given. 20 m seems like a very large amplitude for a wave on a string. :wideeyed:
 
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  • #3
ahaha !. The :wideeyed: is making me laugh. Yeah the question didn't give the units for y. Thanks TSny.
 

1. What is the definition of amplitude of velocity?

The amplitude of velocity refers to the maximum displacement of a particle in a travelling wave from its equilibrium position. It is a measure of the strength or intensity of the wave.

2. How is amplitude of velocity different from amplitude of displacement?

Amplitude of displacement refers to the maximum distance a particle moves from its equilibrium position in a wave, while amplitude of velocity refers to the maximum speed at which the particle moves. They are related but not the same.

3. What factors affect the amplitude of velocity in a travelling wave?

The amplitude of velocity is affected by the amplitude of the wave itself, the frequency of the wave, and the medium through which the wave is travelling. It is also affected by any damping or resistance present in the medium.

4. How is the amplitude of velocity measured in a wave?

The amplitude of velocity can be measured by tracking the displacement of a particle in a wave over a period of time and calculating its maximum velocity. It can also be measured using specialized equipment such as a wave analyzer.

5. What is the relationship between amplitude of velocity and energy in a travelling wave?

The amplitude of velocity is directly proportional to the energy carried by a travelling wave. This means that a higher amplitude of velocity corresponds to a higher energy wave, and vice versa.

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