Originally posted by tvpiano:

I search this site

http://www.sfu.ca/sonic-studio/handbook/Wavelength.html and they said that the lowest C on piano is 32.7 Hz and wave length is 34 feet 6 inches.

If they are correct, can a piano string which its length is much less than 34 feet produce a sound at 32.7 Hz?.

Thanks,[/b]

Wavelength has little to do with the length of the piano string required to produce the sound at 32.7 Hz. Wavelength is related to frequency by the following formula:

velocity of sound = wavelength x frequency

The velocity of sound in air is about 343 m/sec. They obtained the wavelength of 34 feet 6 inches through this equation; the wavelength equals the velocity of sound divided by frequency. This produces an answer of about 10.5 m for the wavelength, which in turn translates to about 34 feet 6 inches.

The lower the frequency of the sound, the longer the string required to produce it and the longer the wavelength. So frequency is inversely proportional to the length L of the string:

L1/L2 = f2/f1

This is assuming that all the strings of the piano have the same mass per unit length. The highest key on the piano has a frequency about 150 times the frequency of the lowest key. So if we let f2 equal the frequency of the highest key and f1 equal the frequency of the lowest key, we have f2/f1 = 150, which means L1/L2 = 150. In other words, the string for the lowest key needs to be 150 times the length of the string for the highest key assuming all the strings were of the same mass per unit length. That means if the string for the highest key were 5 cm, the string for the lowest key would be 7.5 m, which translates to about 25 ft. In order to avoid making pianos this long, the lower strings are made more dense. The velocity of the sound produced from a piano string is related to the tension of the string and the mass per unit length:

velocity = square root (tension/mass per unit length)

So if a string is given a higher mass per unit length, the velocity of the sound produced would be lower, which would decrease the frequency for a particular wavelength.

The wavelength produced by a string of length L is usually fixed; piano strings produce waves that are of fundamental or first harmonic frequency, which means the wavelength is 2L.

This is from my physics notes; I took notes from Giancoli's physics textbook.

Sorry if this is a bit difficult to understand.