Speed of a wave on a string and Frequency of 3rd Harmonic

1. Feb 8, 2014

ddsMom

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

Tension = 400 N
Mass = 4g
Length = .96m
What is the speed of the wave on a string?

What is the frequency of the 3rd harmonic?

2. Relevant equations

v=√T/(m/L)

v=fλ

3. The attempt at a solution

v=√400N/(.004kg/.96m) = 310m/s......am I correct?

f=v/λ
2nd harmonic f=v/(λ/2) = 310/(.96/2) = 646Hz

3rd harmonic f=v/(λ*2/3) = 646/.64 = 1009Hz

Thank you so much for your input. Really trying to learn this!

2. Feb 8, 2014

vela

Staff Emeritus
Yes.

What's $\lambda$? I think you meant L. I got a different answer than you did for the frequency of the third harmonic.

3. Feb 8, 2014

ddsMom

I think I see my mistake. It should read...

f=v/λ
2nd harmonic f=v/(λ/2) = 310/(.96/2) = 646Hz
3rd harmonic f=v/(λ*2/3) = 310/.64 = 484Hz

Is that correct?

4. Feb 8, 2014

vela

Staff Emeritus
No. The frequency should increase with higher harmonics.

5. Feb 8, 2014

ddsMom

That's what I thought. What am I doing wrong???

3rd harmonic f=v/(λ*2/3) = 310/(.96/(2/3)) = 484Hz is my initial formula

6. Feb 8, 2014

vela

Staff Emeritus
Actually, your frequency for the third harmonic is right. The wavelength and therefore the frequency you have for the second harmonic is wrong.

Every time you go up one harmonic, you fit in another half wavelength on the length of the string. So for the first harmonic, you have $1\times\lambda/2 = L$; for the second, you get $2\times\lambda/2 = L$; and so on.

7. Feb 8, 2014

ddsMom

I got it. The frequency of the second harmonic is two times the frequency of the first harmonic. The frequency of the third harmonic is three times the frequency of the first harmonic.

so the answer is 969...I was going about it the hard way.

8. Feb 8, 2014

vela

Staff Emeritus
Nooooo!

9. Feb 8, 2014

ddsMom

Really???

10. Feb 8, 2014

vela

Staff Emeritus
Yes, really. The frequencies aren't simply integer multiples of the fundamental frequency. You were on the right track earlier, but you were making some mistakes.

11. Feb 8, 2014

ddsMom

That would be 310/(3*λ/2) = 310/1.44 = 215.

That doesn't seem correct?

It's been over 20 years since I've had Physics so I definitely appreciate any help.