Distance traveled by a particle in a transverse wave

In summary, the particle moves of harmonic motion from maximum amplitude ##A## to negative maximum amplitude ##-A##. The period ##T=\frac{1}{f}## is equal to the time in which a particle travels a distance ##d=3\cdot A##. I then approximated the mean vertical velocity of the particle ##v_{y}=\frac{3\cdot A}{T}##. However, the result I get is wrong. There must be a problem with the mean velocity, and I will have to look into it further.
  • #1
greg_rack
Gold Member
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Homework Statement
A transverse wave traveling through a medium has a frequency of 5.0 Hz, a wavelength of
4.0 cm and an amplitude of 3.0 cm.
What is the total distance traveled by a particle of the medium in one minute?
Relevant Equations
##v=\lambda f##
##f=\frac{1}{T}##
Taken into account the transverse nature of the wave, I deduce the particle must move of harmonic motion from maximum amplitude ##A## to negative maximum amplitude ##-A##.
The period ##T=\frac{1}{f}## is equal to the time in which a particle travels a distance ##d=3\cdot A##. I then approximated the mean vertical velocity of the particle ##v_{y}=\frac{3\cdot A}{T}##.
Then, multiplying this result per 60 seconds, I should find the distance traveled in a minute... but the result I get is wrong.
There must be a problem with the mean velocity...
 
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  • #2
greg_rack said:
Homework Statement:: A transverse wave traveling through a medium has a frequency of 5.0 Hz, a wavelength of
4.0 cm and an amplitude of 3.0 cm.
What is the total distance traveled by a particle of the medium in one minute?
Relevant Equations:: ##v=\lambda f##
##f=\frac{1}{T}##

Taken into account the transverse nature of the wave, I deduce the particle must move of harmonic motion from maximum amplitude ##A## to negative maximum amplitude ##-A##.
The period ##T=\frac{1}{f}## is equal to the time in which a particle travels a distance ##d=3\cdot A##. I then approximated the mean vertical velocity of the particle ##v_{y}=\frac{3\cdot A}{T}##.
Then, multiplying this result per 60 seconds, I should find the distance traveled in a minute... but the result I get is wrong.
There must be a problem with the mean velocity...
"The period ##T=\frac{1}{f}## is equal to the time in which a particle travels a distance ##d=3\cdot A##. I then approximated the mean vertical velocity of the particle ##v_{y}=\frac{3\cdot A}{T}##"
No, it raise up A, returns again to equilibrium position by traveling A, it goes down A, and returns, again, traveling A! It is not 3, it is four.
 
  • #3
LCSphysicist said:
"The period ##T=\frac{1}{f}## is equal to the time in which a particle travels a distance ##d=3\cdot A##. I then approximated the mean vertical velocity of the particle ##v_{y}=\frac{3\cdot A}{T}##"
No, it raise up A, returns again to equilibrium position by traveling A, it goes down A, and returns, again, traveling A! It is not 3, it is four.
Thank you very much, that's right
 
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Related to Distance traveled by a particle in a transverse wave

1. What is the definition of "distance traveled" in a transverse wave?

The distance traveled by a particle in a transverse wave refers to the total displacement of the particle from its original position as the wave passes through it. This distance is measured in the direction perpendicular to the direction of wave propagation.

2. How is the distance traveled by a particle in a transverse wave related to its amplitude?

The distance traveled by a particle in a transverse wave is directly proportional to its amplitude. This means that as the amplitude of the wave increases, the distance traveled by the particle also increases.

3. Does the distance traveled by a particle in a transverse wave depend on the medium it is traveling through?

Yes, the distance traveled by a particle in a transverse wave is affected by the properties of the medium it is traveling through. This includes factors such as density, elasticity, and temperature.

4. How is the distance traveled by a particle in a transverse wave affected by the frequency of the wave?

The distance traveled by a particle in a transverse wave is inversely proportional to the frequency of the wave. This means that as the frequency increases, the distance traveled by the particle decreases.

5. Can the distance traveled by a particle in a transverse wave be negative?

No, the distance traveled by a particle in a transverse wave cannot be negative. This is because the distance is measured as a displacement from the particle's original position, and displacement is always a positive value.

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