A transverse wave traveling through a medium versus a particle of the medium

[User1265]

Homework Statement

A transverse wave travelling 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 travelled by a particle of the medium in one minute?

Relevant Equations

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I imagine a particle traveling across 1 wave cycle. The total vertical distance traveled across the wave cycle is 4 x the amplitude of the wave. The total vertical distance traveled in 1 minute:

5 cycles in 1 second, thus 5x60 cycles in a minute

then 4 x amplitudes effectively traveled per wave cycle = 4 x 3cm = 12cm distance traveled vertically per wave cycle

total distance traveled (vertically) by particle in the medium for a minute = 12 x 5x60 = 12x300 = 3600cm

The question I have is : Q1 The particle travels the wave - as the wave progresses through the medium, so why is it that the particle only travels in the vertical direction (ocsillating up and down) but we do not calculate the horizontal distance the particle travels (in the direction of the wave propagation) ?
Q2 Does a particle of a medium travel any horizontal distance/ in the direction of wave propagation at all if a wave progresses through the particle/ through the medium?

Q3 If it is true that a particle of a medium does not progress in the horizontal direction / the direction the wave propagates in a medium, then is it wrong to think of the particle traveling 1 wave cycle?

Q4 Is it better to think of a particle of fixed horizontal coordinate,moving up and down as a wave (of 1 cycle) progresses through the medium/and particle?

 

[Steve4Physics]

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?
...

Your answer to the original question shows a good understanding. To help you with your 4 questions...

Q1 The particle travels the wave - as the wave progresses through the medium, so why is it that the particle only travels in the vertical direction (oscillating up and down) but we do not calculate the horizontal distance the particle travels (in the direction of the wave propagation)?

For a transverse wave traveling horizontally there is no horizontal movement. Think how a ‘Mexican wave’ works in a football crowd. Watch this animation:
https://gifimage.net/transverse-wave-animation-gif-4/
and follow a red dot.

Q2 Does a particle of a medium travel any horizontal distance in the direction of wave propagation at all if a wave progresses through the particle/ through the medium?

No. Same as Q1.

And you can’t say a wave travels 'through the particle'. A wave is a moving pattern of the particles.

But if the medium is moving (e.g. a water wave on the surface a flowing river) the particles are obviously also moving along with the medium (because the medium IS the collection of particles).

Q3 If it is true that a particle of a medium does not progress in the horizontal direction / the direction the wave propagates in a medium, then is it wrong to think of the particle traveling 1 wave cycle?

It could be misleading. But it is not wrong, providing that ‘travelling’ is understood to refer to motion in the direction perpendicular to the direction of propagation. But the particle’s displacement is zero after each cycle.

Q4 Is it better to think of a particle of fixed horizontal coordinate, moving up and down as a wave (of 1 cycle) progresses through the medium/and particle?

It is clearer – it accurately describes what happens in a (horizontal) transverse wave.

Other notes:

The direction of propagation doesn’t have to be horizontal. But whatever the direction is, in a transverse wave the particles oscillate perpendicular to it.

For longitudinal waves, particles oscillate backwards and forwards parallel to the direction of propagation. But each particle is still back at its initial position after each cycle..

Waves don’t have to consist of patterns created by oscillating particles. In an electromagnetic wave (which is transverse) it is the electric and magnetic fields that oscillate, but this is harder to visualise.

 

[haruspex]

Does a particle of a medium travel any horizontal distance/ in the direction of wave propagation at all if a wave progresses through the particle/ through the medium?

It certainly can. See e.g. Fig 4.18 at https://manoa.hawaii.edu/exploringourfluidearth/physical/waves/wave-energy-and-wave-changes-depth.
If I generate a wave in a rope, the rope barely changes length, so the motions of individual elements of the rope must involve some longitudinal component.

 

[Steve4Physics]

It certainly can. See e.g. Fig 4.18 at https://manoa.hawaii.edu/exploringourfluidearth/physical/waves/wave-energy-and-wave-changes-depth.
If I generate a wave in a rope, the rope barely changes length, so the motions of individual elements of the rope must involve some longitudinal component.

Good point. The OP should note that in such real-world cases we're dealing with a combination of transverse and longitudinal waves, as opposed to a 'perfect' (ideal) transverse wave.

 

[User1265]

Your answer to the original question shows a good understanding. To help you with your 4 questions...

Q1 The particle travels the wave - as the wave progresses through the medium, so why is it that the particle only travels in the vertical direction (oscillating up and down) but we do not calculate the horizontal distance the particle travels (in the direction of the wave propagation)?

For a transverse wave traveling horizontally there is no horizontal movement. Think how a ‘Mexican wave’ works in a football crowd. Watch this animation:
https://gifimage.net/transverse-wave-animation-gif-4/
and follow a red dot.

Q2 Does a particle of a medium travel any horizontal distance in the direction of wave propagation at all if a wave progresses through the particle/ through the medium?

No. Same as Q1.

And you can’t say a wave travels 'through the particle'. A wave is a moving pattern of the particles.

But if the medium is moving (e.g. a water wave on the surface a flowing river) the particles are obviously also moving along with the medium (because the medium IS the collection of particles).

Q3 If it is true that a particle of a medium does not progress in the horizontal direction / the direction the wave propagates in a medium, then is it wrong to think of the particle traveling 1 wave cycle?

It could be misleading. But it is not wrong, providing that ‘travelling’ is understood to refer to motion in the direction perpendicular to the direction of propagation. But the particle’s displacement is zero after each cycle.

Q4 Is it better to think of a particle of fixed horizontal coordinate, moving up and down as a wave (of 1 cycle) progresses through the medium/and particle?

It is clearer – it accurately describes what happens in a (horizontal) transverse wave.

Other notes:

The direction of propagation doesn’t have to be horizontal. But whatever the direction is, in a transverse wave the particles oscillate perpendicular to it.

For longitudinal waves, particles oscillate backwards and forwards parallel to the direction of propagation. But each particle is still back at its initial position after each cycle..

Waves don’t have to consist of patterns created by oscillating particles. In an electromagnetic wave (which is transverse) it is the electric and magnetic fields that oscillate, but this is harder to visualise.

Thanks this is really helpful!