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

[ddsMom]

Homework Statement

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?

Homework Equations

v=√T/(m/L)

v=fλ

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

Are my answers correct?

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

 

[vela]

Homework Statement

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?

Homework Equations

v=√T/(m/L)

v=fλ

The Attempt at a Solution

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

Yes.

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

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

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

 

[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?

 

[vela]

No. The frequency should increase with higher harmonics.

 

[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

 

[vela]

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.

 

[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.

Thank you for your time!

 

[vela]

Nooooo!

 

[ddsMom]

Really?

 

[vela]

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.

 

[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.