# Second harmonic is the length of the string???

#### Ineedhopenow

##### Full Member
5+ Year Member
"Second harmonic is the length of the string"

A string is 0.1 meter long. The speed of the string is 100 m/s. What's the frequency of the first harmonic?

0.1=(2)W/2 so W=0.1 m, then 100m/s= f*0.1, so f= 1000 Hz

But my book states that my answer is wrong. It states that the answer is 500 Hz.

That means it ignored the rule quoted above!
0.1=(1)W/2 so W=0.2 m, then 100m/s= f*0.2, so f= 500 Hz

I'm looking for the TRUTH!!! Please enlighten me.

#### chiddler

##### Full Member
10+ Year Member
first harmonic = fundamental frequency, so n = 1.

F = n(v/2L) = 100/(2*0.1) = 100*0.2 = 500

I think you mistook first harmonic to be the first overtone, which is different. but i'm not sure because it's hard to decipher how you set up your equation o_o

how did you set it up?

#### Ineedhopenow

##### Full Member
5+ Year Member
Thanks chiddler, I did the same thing as you as shown on the second solution, however my confusion lies in the quoted statement.

#### Ineedhopenow

##### Full Member
5+ Year Member
Since the second harmonic determines the length of the string, and we're given the length of the string. Shouldn't we use n=2 when solving this problem?

#### chiddler

##### Full Member
10+ Year Member
Thanks chiddler, I did the same thing as you as shown on the second solution, however my confusion lies in the quoted statement.

oh sorry.

the second harmonic is n=2. &#955;= 2L/n, therefore, &#955; = L when n = 2.

but how does this relate to the latter part of your question?

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