# How to solve this standing wave problem?

Question:

"A string is held under 5.00N of tension, with a distance between two bridges of 50.0cm. A signal generator can produce vibrations in the string, but is broken and does not work for frequencies below 100Hz. Resonance is observed at 125Hz, 187.5Hz, and 250Hz. Calculate the speed of the progressive wave along the string".

Not sure how to get the answer as by assuming f = 125hz is the fundamental frequency, I used the equation to get mass per unit length = 1/3125

From there I subbed it into = T/mass per unit length to get c = 125ms^-1 which was wrong...

Any ideas...
Original post by MonoAno555

Question:

"A string is held under 5.00N of tension, with a distance between two bridges of 50.0cm. A signal generator can produce vibrations in the string, but is broken and does not work for frequencies below 100Hz. Resonance is observed at 125Hz, 187.5Hz, and 250Hz. Calculate the speed of the progressive wave along the string".

Not sure how to get the answer as by assuming f = 125hz is the fundamental frequency, I used the equation to get mass per unit length = 1/3125

From there I subbed it into = T/mass per unit length to get c = 125ms^-1 which was wrong...

Any ideas...

When several resonance frequencies are given, it is advisable not to assume the fundamental frequency.
We can also “show” that 125 Hz cannot be the fundamental frequency.
Say that f1 is the fundamental frequency, then the higher harmonics or resonance frequencies can be expressed as multiple of f1.
f2 = 2f1, f3 = 3f1 , etc…

The product of the resonance frequency and wavelength is equal to the speed of the progressive wave.
For different frequency and wavelength, the speed of the progressive wave remains the same.
So we have
$c = f_n \times \lambda_n$

You can then set up 2 equations with
$\lambda_n = \dfrac{2l}{n}$

to solve to find the n.

After solving for n, finding the speed of the progressive wave should be “obvious”, if not you can post your working.
What equation did you use to find the mass per unit length (μ) given the data available in the question?
[quote(Original post by "The Dal Fade")]What equation did you use to find the mass per unit length (μ) given the data available in the question?

If you are asking how to solve the Isaac Physics problem, mass per unit length is not required to solve the problem.

What is needed here is to note that when the frequency and wavelength change, the “speed” of the wave remains unchanged.
I was just wondering how they managed to find mass per unit length (1/3125) given the data available in the question (I understand that mass per unit length is not needed to find the answer).

Original post by Eimmanuel
[quote(Original post by "The Dal Fade")]What equation did you use to find the mass per unit length (μ) given the data available in the question?

If you are asking how to solve the Isaac Physics problem, mass per unit length is not required to solve the problem.

What is needed here is to note that when the frequency and wavelength change, the “speed” of the wave remains unchanged.