Sound & Music, String Frequency

[Torrie]

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.

 

[gneill]

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?

 

[Torrie]

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?

 

[gneill]

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?