Finding the relationship between wave speed and tension in a standing wave

In summary, the problem is to find the relationship between wave speed and tension for a standing wave in a string with fixed ends. The experiment involved using a vibrator with adjustable frequency attached to one end of the string, while weights could be attached to the other end suspended across a pulley. The given data includes the string length of 1.62m and a frequency of 48.2 Hz. The recorded results show the tension and number of nodes for each trial. To find the wavelength, the formula y = (x-1)/2 was used, where x is the number of nodes. The calculated wavelengths were then used to calculate the wave speeds using the formula v=fλ. Another formula, v = √(t/
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Homework Statement


The problem is the same as the title; to find the relation between wave speed and tension for a standing wave in a string. (Fixed ends)

Given data (from the experiment)

String length = 1.62m, mass is negligible
Frequency = 48.2 Hz
Basically one end of the string was attached to a vibrator with adjustable frequency and the other end suspended across a pulley from where weights could be attached.

These are the recorded results:
Tension :: Number of nodes
0.981 - 4
1.962 - 3
3.924 - 2
7.848 - 1

Homework Equations


v=fλ
v = √(t/μ)

y = (x-1)/2
I used this last one to find the *number of wavelengths* (not the wavelength itself) in the standing wave where x is the number of nodes.

The Attempt at a Solution



I used the number of nodes to calculate the wavelength (length provided as 1.62)
Tension :: wavelength
0.981 - 1.08
1.962 - 1.62
3.924 - 3.24
7.848 - 6.48

And I used
v=fλ, where f = 48.2 to calculate wave speeds. I got 52.06; 78.08; 156.17; 312.34.

I also used v = √(t/μ) to calculate a theoretical speed to plot against the experimental, but I got the same value every time by that method (around 3.967 ms-1).

Well, at the moment, I just want to know what the relationship between tension and wave speed SHOULD be theoretically. (just an equation)
I'm hopelessly confused right now...

Edit: If I can understand the relation I should be able to plot a graph for my experimental values, hopefully I can make some sense out of the results

Edit 2: I thought of this earlier but I keep loosing track since I have no firm grasp on the concept
v = √(t/μ)
Isn't THIS the relation between wave speed and tension itself? :s
 
Last edited:
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  • #2
Starting from the last question, yes ##v=\sqrt{T/\mu}## is the correct equation relating the propagation speed to the tension. For a fixed tension, you get a fixed speed. If you vary the frequency, you simultaneously vary the wavelength because the product ##\lambda f## is fixed. Is this an experiment where you fixed the frequency and varied the tension until you got a certain number of nodes? Please describe what you did to get the numbers you posted. Specifically, what did you do to get the pairs of tensions and wavelengths. Also, please remember to attach units to any numbers that have dimensions. This is particularly important in lab experiments.
 

What is a standing wave?

A standing wave is a type of wave that oscillates in a fixed position, rather than travelling through space. It is formed by the interference of two waves with the same frequency and amplitude, travelling in opposite directions.

What is the relationship between wave speed and tension in a standing wave?

The relationship between wave speed and tension in a standing wave is directly proportional. This means that as tension increases, wave speed also increases. Similarly, as tension decreases, wave speed decreases.

How is wave speed measured in a standing wave?

Wave speed in a standing wave can be measured by calculating the wavelength and frequency of the wave. The wave speed is equal to the product of the wavelength and frequency.

How does tension affect the amplitude of a standing wave?

Tension does not have a direct effect on the amplitude of a standing wave. However, it can indirectly affect the amplitude by changing the wave speed. As mentioned before, tension and wave speed are directly proportional, so a change in tension will result in a change in wave speed, which can then affect the amplitude of the standing wave.

What factors can affect the relationship between wave speed and tension in a standing wave?

The relationship between wave speed and tension in a standing wave can be affected by factors such as the properties of the medium, the frequency of the wave, and the shape of the medium. For example, the type of material and its density can influence the tension and therefore affect the wave speed.

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