I have a question concerning waves. What effect does increasing the tension in a vibrating string have upon wavelength? I was thinking that as the weight increases more standing waves are created. As more standing waves are created, the wavelength decreases.

I have one more quick question, we were asked to graph F (force) vs 1/n^2. The n is referring to the number of loops in 1/n^2. Could you tell me what 1/n^2 might stand for when graphing it verses Force.
Thank you

Increasing tension makes for increased wave velocity. The wave equation

freq*wavelength = velocity of propagation
so if velocity increases, wavelength increases, but on a fixed length string, that means fewer wavelengths

To explain the effect of increasing tension in a vibrating string on the wavelength, let's consider the wave equation:

frequency * wavelength = velocity of propagation

As you correctly mentioned, increasing tension in the string will increase its wave velocity. However, in the case of a fixed length string, increasing the wave velocity means that the wavelength will become longer. This is because the total length of the string remains constant, but the number of wavelengths that fit in that length decreases.

Think of it this way: if the tension is low, the waves on the string will be slower and will need more wavelengths to fit in the same length. But when tension increases, the wave speed increases, resulting in longer wavelengths. So, your initial intuition that increasing tension leads to a decrease in wavelength is not correct.

Regarding your second question about graphing F (force) vs 1/n^2, let's break it down. In this case, "n" is referring to the number of loops. The term 1/n^2 is actually the reciprocal square of "n."

When graphing 1/n^2 against Force, it suggests that there might be an inverse square relationship between the number of loops (1/n^2) and the force. It's possible that the force decreases as the number of loops increases (or vice versa) in an inverse square manner.

To get the answer, you can plot different values of 1/n^2 on the x-axis and the corresponding values of Force on the y-axis. Then, see if there is a pattern or trend that emerges. If the relationship is inverse square, you would expect the data points to roughly follow a curve that decreases rapidly as 1/n^2 increases.

Remember, in these situations, data analysis and graphing are crucial to understanding the relationship between variables.