# Assumptions for string vibrator system

• member 731016
In summary: I note that in some cases there is a real node just to the right, in others a virtual node just to the left. It would be interesting to predict that displacement as a function of the parameters.Thank you @haruspex, @BvU, @nasu, and @berkeman for your replies!Sorry for not posting earlier. Here is the figure requested. In summary, when the frequency is slowly increased, the node is fixed at the vibrator end due to resonance.
member 731016
Homework Statement
Relevant Equations
For this,

Is it possible to calculate the time it takes for the initial antinode at the string vibrator to become a node in the transient phase of the system? Also do we assume that once the system has reached steady state, that the mass has such a large inertia that it is stationary so acts as a fixed boundary reflecting the waves at a 180-degree phase shift relative to the incident traveling waves?

Many thanks!

ChiralSuperfields said:
Is it possible to calculate the time it takes for the initial antinode at the string vibrator to become a node in the transient phase of the system? Also do we assume that once the system has reached steady state, that the mass has such a large inertia that it is stationary so acts as a fixed boundary reflecting the waves at a 180-degree phase shift relative to the incident traveling waves?

Many thanks!
Not sure I understand your first question. The frequency is increased slowly, meaning that when arriving at any given frequency the transient phase to steady state is negligible.
Yes, the movement of the mass is also considered negligible here.

member 731016
Hi,
ChiralSuperfields said:
Is it possible to calculate the time it takes for the initial antinode at the string vibrator to become a node in the transient phase of the system?
That point is as good as fixed. Check with fig 16.29
ChiralSuperfields said:
Also do we assume that once the system has reached steady state, that the mass has such a large inertia that it is stationary so acts as a fixed boundary reflecting the waves at a 180-degree phase shift relative to the incident traveling waves?
The fixed point is at the pulley.

member 731016
How would you have a node at the vibrator end? And where is figure 29? Does it show a node at the vibrator end?

berkeman and member 731016
nasu said:
How would you have a node at the vibrator end?
Yeah, I don't get that either. How do you drive vibrations on a string from a node?

member 731016
This is practical physics. The string resonates and the deviations from equilibrium at antinodes are much greater than at the vibrator end, so fapp (for all practical purposes) that end is a node. (Thorough experimentation can reveal how near the virtual node is further to the left).

##\ ##

member 731016, nasu and haruspex
BvU said:
The string resonates and the deviations from equilibrium at antinodes are much greater than at the vibrator end, so fapp (for all practical purposes) that end is a node. (Thorough experimentation can reveal how near the virtual node is further to the left).
Huh, TIL. Thanks @BvU

member 731016
nasu said:
Does it show a node at the vibrator end?
Calling my bluff eh ?
My reputation is in the hands of @ChiralSuperfields

##\ ##

member 731016
I asked this before you posted your video. This is better than figure 29, whatever that is.

member 731016
I have played several times with this PHET simulation but I have not relized (until now) that by using a small amplitude of one end you can produce a much higher amplitude at the node.
So, it works even for a simulation, not just in the real world.

member 731016 and haruspex
nasu said:
I have played several times with this PHET simulation but I have not relized (until now) that by using a small amplitude of one end you can produce a much higher amplitude at the node.
So, it works even for a simulation, not just in the real world.

I note that in some cases there is a real node just to the right, in others a virtual node just to the left. It would be interesting to predict that displacement as a function of the parameters.

member 731016

## What is a string vibrator system?

A string vibrator system is a physical setup used to study the vibrations and wave phenomena in a stretched string. It typically involves a string fixed at both ends, with a mechanical vibrator at one end that induces periodic motion, causing the string to oscillate and form standing waves.

## What are the key assumptions for analyzing a string vibrator system?

The key assumptions include: (1) The string is perfectly flexible and inextensible, (2) The tension in the string is constant and uniform along its length, (3) The amplitude of vibrations is small compared to the length of the string, (4) The effects of air resistance and damping are negligible, and (5) The string has uniform linear mass density.

## Why is it assumed that the string is perfectly flexible and inextensible?

This assumption simplifies the mathematical modeling by ensuring that the string can bend without resistance and does not stretch under tension. It allows the use of linear wave equations to describe the motion of the string accurately.

## How does constant tension affect the behavior of the string vibrator system?

Constant tension ensures that the wave speed along the string remains uniform, which is crucial for forming predictable standing wave patterns. Variations in tension would lead to changes in wave speed, complicating the analysis and potentially disrupting the formation of standing waves.

## What is the significance of assuming small amplitude vibrations?

Assuming small amplitude vibrations allows for the use of linear approximations in the wave equations. This means that the restoring force is directly proportional to the displacement, leading to simple harmonic motion. Large amplitudes would introduce nonlinear effects, making the system more complex to analyze.

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