How Does String Length and Tension Affect Harmonics and Overtones?

[nblu]

Hi, thank you for reading this.

The question is;

"A guitar string 60.0 cm in length, with a diameter of 1.40 mm and a tension of 289 N,
emits a note with a frequency of 147 Hz. Find the frequency in each of the following
situations"

d) The string produces the third harmonic of the 147 Hz fundamental frequency.
e) The string emits the third overtone of its 147 Hz fundamental.

There were 3 leading question which were just "substitute" and solve into the
equation however, the last two questions are giving me an headache.

For instance, in "D", it mentions the third harmonic of the 147 Hz, so I've began with;
3 (147Hz) = 441 Hz, then I have no idea what to do next..

Could anybody please give me some advice?

 

[dynamicsolo]

Hi, thank you for reading this.

The question is;

"A guitar string 60.0 cm in length, with a diameter of 1.40 mm and a tension of 289 N,
emits a note with a frequency of 147 Hz. Find the frequency in each of the following
situations"

d) The string produces the third harmonic of the 147 Hz fundamental frequency.
e) The string emits the third overtone of its 147 Hz fundamental.

There were 3 leading question which were just "substitute" and solve into the
equation however, the last two questions are giving me an headache.

For instance, in "D", it mentions the third harmonic of the 147 Hz, so I've began with;
3 (147Hz) = 441 Hz, then I have no idea what to do next..

Could anybody please give me some advice?

It looks like all they're asking you to do is apply the definitions of "nth harmonic" and "nth overtone". You should be correct for part (d), in that the third harmonic has 3 times the frequency of the fundamental frequency for the string.

As for part (e), check your source's definitions, but usually, the overtones are counted above the fundamental frequency. So the sequence goes fundamental frequency, first overtone, second overtone, third overtone, etc. So the third overtone would be which harmonic? That will tell you its frequency.

 

[nblu]

It looks like all they're asking you to do is apply the definitions of "nth harmonic" and "nth overtone". You should be correct for part (d), in that the third harmonic has 3 times the frequency of the fundamental frequency for the string.

As for part (e), check your source's definitions, but usually, the overtones are counted above the fundamental frequency. So the sequence goes fundamental frequency, first overtone, second overtone, third overtone, etc. So the third overtone would be which harmonic? That will tell you its frequency.

Hi dynamic, thanks for your comment, again :P
Third Overtone is the fourth harmonic which would be calculated as 4 (147Mz), right?

I've calculated both answers already
but I didn't think it was supposed to be that simple...lol

 

[Doc Al]

For instance, in "D", it mentions the third harmonic of the 147 Hz, so I've began with;
3 (147Hz) = 441 Hz, then I have no idea what to do next..

That's all there is to it, as far as I can see. For "E", what's the definition of overtone?

 

[nblu]

That's all there is to it, as far as I can see. For "E", what's the definition of overtone?

According to a chart that I've looked up;

Third Overtone = Fourth Harmonic = 4(fo) = Pitch of A note hehe