How Long Is the Piano String for the 3rd Harmonic?

[xuhhad]

The 3rd harmonic on a piano string occurs when a 45.0 cm wave is produced. How long is the string.

This question is really confusing can i get some leads to help me out please and thank u

 

[CWatters]

Make three drawings showing a string vibrating at the first, second and third harmonic.
Hint: Third harmonic has three antinodes.

http://en.wikipedia.org/wiki/Vibrating_string

Mark the wave length on the drawing of the third harmonic.
http://en.wikipedia.org/wiki/Wavelength

The question is presumably telling you that one wavelength is 45cm.

Apply basic maths to calculate the length of the string.

I'll let you work it out but I make the answer a number between 60cm and 70cm.

 

[CWatters]

PS See also:

https://www.physicsforums.com/showthread.php?t=8128

 

[xuhhad]

OK i understand but i still don't no what formula to use.

 

[CWatters]

No formula is required. Scale from the drawing.

One wave length = two half wave lengths = 45cm

So three half wave lengths = 3/2 * 45cm = 67.5cm