# Homework Help: Tension in a vibrating string at a given frequency

1. May 6, 2010

### sfdrew

1. The problem statement, all variables and given/known data

A 4.0g string of 0.67m length is vibrating at 300Hz in the third harmonic. The speed of sound in the air is 344 m/s. What is the tension in the string in SI units.

A) 110
B) 88
C) 69
D) 130
E) 150

2. Relevant equations

//frequency is equal to velocity over wavelength
f = v/lambda

3. The attempt at a solution

So, f sub n = nf sub 1, the fundamental frequency. That means that I can rewrite this using the frequency equation as...

100*2*L*sqrt(m/L) = sqrt(T)

=> 100*2*0.67*.0773 = sqrt(T)

=> 10.35 = sqrt(T)

=> (10.35)^2 = T

=> T = 107.2

107.2 is closest to 110, which is choice A, but it isn't exact and I didn't use the speed of sound in the air quantity for anything. I'm not sure if I did this problem correctly or not? Can anybody help?

Last edited: May 6, 2010
2. May 6, 2010

### Stonebridge

I get the same answer as you.
For this calculation the speed of sound in air is not needed.
As the relevant data is given to 2 significant figures, the answer of 110N is correct to the same level of precision/certainty.

3. Mar 11, 2011