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

AI Thread Summary
The discussion centers on calculating the length of a piano string for the 3rd harmonic, which corresponds to a wavelength of 45 cm. The string's length can be determined by understanding that the third harmonic has three antinodes, leading to the formula where three half wavelengths equal the string length. Specifically, three half wavelengths amount to 67.5 cm. Participants emphasize using drawings to visualize the harmonics and suggest that no complex formulas are necessary for the calculation. The final calculated length of the string is 67.5 cm.
xuhhad
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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
 
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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.
 
Last edited:
OK i understand but i still don't no what formula to use.
 
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
 

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