Graph for sinusoidal wave travelling to the left

In summary, the waveform drawn in red is incorrect because the basketball will drift slowly to the left in the direction of wave propagation. The waveform drawn in black is correct because the basketball will move quickly to the left in the direction of wave propagation.
  • #1
ChiralSuperfields
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Homework Statement
Please see below
Relevant Equations
Please see below
For part(a) of this problem,
1675801220480.png

The solution is,
1675801355607.png

I don't understand why they assume on the graph where that the waveform is during it's phase. For example, could it not also be correctly drawn as shown in red:
1675801695226.png

Could it not?

Many thanks!
 

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  • #2
Not an expert on the subject, but you might want to reread the second sentence of the problem, again.
 
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  • #3
"... travelling in the negative x direction..." & "...the element has a positive velocity here."
What exactly do you think those mean in terms of y(0)?
 
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  • #4
DaveE said:
"... travelling in the negative x direction..." & "...the element has a positive velocity here."
What exactly do you think those mean in terms of y(0)?
Thank you for you reply @DaveE! I'm not sure what those means in terms of y(0)
 
  • #5
hmmm27 said:
Not an expert on the subject, but you might want to reread the second sentence of the problem, again.
Thank you for you reply @hmmm27 !
 
  • #6
Callumnc1 said:
Thank you for you reply @DaveE! I'm not sure what those means in terms of y(0)
OK let's consider a more concrete example. Imagine a surface wave in the middle of the ocean. You see a wave maximum moving from right to left. At a place you call "0" you drop a basketball. How does it move as the wave goes by.
 
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  • #7
DaveE said:
OK let's consider a more concrete example. Imagine a surface wave in the middle of the ocean. You see a wave maximum moving from right to left. At a place you call "0" you drop a basketball. How does it move as the wave goes by.
Thank you for your reply @DaveE!

I think in an ideal case we assume that the ocean wave is traverse. Therefore, the basketball should not move since it should act as another element of the medium so will move vertically in simple harmonic motion with the other elements.

However, for a more realistic case, surface waves are made up of traverse and longitudinal waves, so the basketball will drift very slowly to the left in the direction of wave propagation along the ocean current.
 
  • #8
Consider only the transverse (vertical) motion of the basketball.
 
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  • #9
The point has a positive velocity. Will it’s value be larger, smaller or the same at the next instant in time?
 
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  • #10
Thank you for your replies @hutchphd and @Frabjous !

So, if the basketball moves in transverse motion, then assuming the basketball is dropped at the wave maximum, then its transverse speed will be greater at the next instant of time.
 
  • #11
Callumnc1 said:
Thank you for your reply @DaveE!

I think in an ideal case we assume that the ocean wave is traverse. Therefore, the basketball should not move since it should act as another element of the medium so will move vertically in simple harmonic motion with the other elements.

However, for a more realistic case, surface waves are made up of traverse and longitudinal waves, so the basketball will drift very slowly to the left in the direction of wave propagation along the ocean current.
OK, so let's put some giant graph paper in the ocean. The vertical motion can be in the y direction, the direction of wave travel (perpendicular to the wave peaks) can be in the -x direction, because they said the wave moves that way. Now reconsider those two functions you drew. Which best matches what the basketball does?
 
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  • #12
To expand a bit on what others have said:

Remember the motion of an element at a particular x-position is purely transverse.

https://www.physicsforums.com/attachments/1675801695226-png.321914/

You are told that when at t=0. the element at x=0 has a positive (‘upwards’) velocity.

And you are told the waveform moves left.

Ask yourself (or sketch) where the red and black waveforms will be a short time later.

You should then see why the red waveform isn't correct but the black one is.
 
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  • #13
Callumnc1 said:
Thank you for your replies @hutchphd and @Frabjous !

So, if the basketball moves in transverse motion, then assuming the basketball is dropped at the wave maximum, then its transverse speed will be greater at the next instant of time.
Is the wave higher or lower at the next instant in time?
 
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  • #14
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1. What is a sinusoidal wave travelling to the left?

A sinusoidal wave travelling to the left is a type of wave that moves in a leftward direction and has a shape that resembles a sine wave. It is a type of transverse wave, meaning that the particles of the medium (such as air or water) move perpendicular to the direction of the wave's motion.

2. How is a sinusoidal wave travelling to the left represented on a graph?

A sinusoidal wave travelling to the left is typically represented on a graph with the x-axis representing time and the y-axis representing displacement or amplitude. The graph will show a series of peaks and troughs that correspond to the crests and troughs of the wave.

3. What factors affect the shape of a sinusoidal wave travelling to the left?

The shape of a sinusoidal wave travelling to the left is affected by several factors, including the frequency of the wave (how many cycles occur per unit of time), the amplitude (the height of the wave), and the wavelength (the distance between two consecutive crests or troughs).

4. How does a sinusoidal wave travelling to the left transfer energy?

A sinusoidal wave travelling to the left transfers energy through the medium it is travelling in. As the wave moves, it causes particles in the medium to vibrate, transferring energy from one particle to the next. This transfer of energy is what allows the wave to propagate through the medium.

5. What real-life phenomena can be described by a sinusoidal wave travelling to the left?

Sinusoidal waves travelling to the left can be observed in many real-life phenomena, including sound waves, water waves, and electromagnetic waves. These waves are used in various applications such as communication, navigation, and medical imaging.

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