Sound & Music, String Frequency

AI Thread Summary
The discussion revolves around calculating the frequency of the second mode of a string with specific parameters. The tension is 52 N, the mass per unit length is 1.2 g/m, and the string length is 0.50 m. The correct formula involves calculating the wave speed (Vs) using the tension and mass per unit length, leading to a frequency calculation. After correcting a typographical error from "sort" to "sqrt," the frequency of the second mode is determined to be 416.33 Hz. Participants also highlight the importance of significant figures in reporting results.
Torrie
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Homework Statement


Suppose a string is 0.50 m long, it has a mass per unit length of 1.2 g/m, and it is under a tension of 52 N. What is the frequency of the second mode of this string? Express your answer in the SI unit for frequency?

Homework Equations


f = Vs/2L Vs = sqrt (F/μ)

The Attempt at a Solution


I attempt to answer the second equation first to get Vs. Vs = sort (52 N/.0012 kg/m) And then plug 43333.33 into 43333.33/ 2(.50), and my answer is obviously wrong.
 
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Torrie said:
I attempt to answer the second equation first to get Vs. Vs = sort (52 N/.0012 kg/m) And then plug 43333.33 into 43333.33/ 2(.50), and my answer is obviously wrong.

No doubt the "sort" was meant to be "sqrt". Did you forget to take the square root?
 
It was meant to be sqrt. Thank you so much!
So the answer then is 208.17. Which means the frequency of the second mode is 416.33 Hz?
 
Torrie said:
It was meant to be sqrt. Thank you so much!
So the answer then is 208.17. Which means the frequency of the second mode is 416.33 Hz?
Looks good!

You might want to be careful about specifying too many significant figures in any result you hand in. How many significant figures does your given data suggest that you use?
 

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