- #1

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- Homework Statement:
- Find the velocity of waves in a given string.

- Relevant Equations:
- frequency*wavelength=velocity

Hello: Let's say you have a string and get data by changing the frequency a transverse wave in the string to get different standing modes. You measure the wavelength of each mode for each frequency. That is, the data you get are frequency and wavelength. Now, you are trying to find the velocity of the waves in the string.

I can see two ways to do this, but the second method gives a nonsensical answer and I don't know why!

(1) Method one: Plot frequency on the y-axis and 1/wavelength on the x-axis. Draw a best fit line. The slope of the best-fit line with be the velocity since the equation is: f =v* (1/wavelength)

(2) Method two: Plot frequency on the y-axis and wavelength on the x-axis. Then take the area under the curve to find the velocity since f*wavelength=velocity.

The problem I have with method two is that if you add more data points, the area under the curve will increase! That is, the velocity will increase with more data points... and that makes no sense! The velocity is the the velocity! It should not increase if you add more data.

Can someone please explain what the area under the curve of a frequency vs. wavelength curve represents and what is wrong with the calculation in method two??

Thanks!

I can see two ways to do this, but the second method gives a nonsensical answer and I don't know why!

(1) Method one: Plot frequency on the y-axis and 1/wavelength on the x-axis. Draw a best fit line. The slope of the best-fit line with be the velocity since the equation is: f =v* (1/wavelength)

(2) Method two: Plot frequency on the y-axis and wavelength on the x-axis. Then take the area under the curve to find the velocity since f*wavelength=velocity.

The problem I have with method two is that if you add more data points, the area under the curve will increase! That is, the velocity will increase with more data points... and that makes no sense! The velocity is the the velocity! It should not increase if you add more data.

Can someone please explain what the area under the curve of a frequency vs. wavelength curve represents and what is wrong with the calculation in method two??

Thanks!