Why Eight Feet?
The particular length "eight feet" is based on the approximate length of an organ pipe sounding the pitch two octaves below middle C, the bottom note on an organ keyboard. This may be calculated as follows.
Physics tells us that if a pipe is open at both ends, as is true of most organ pipes, its fundamental frequency f can be calculated (approximately) as follows:
where
- f = fundamental frequency
- v = the speed of sound
- l = the length of the pipe
If v is assumed to be 1130 feet per second (the speed of sound at sea level, with temperature 70 degrees Fahrenheit), and the pipe length l is assumed to be eight feet, then the formula yields the value of 70.6 hertz (Hz; cycles per second). This is not far from the pitch of the C two octaves below 440 Hz, which (when concert pitch is set at A = 440 Hz) is 65.4 Hz. The discrepancy may be related to various factors, including effects of pipe diameter, the historical differing definitions of the length of the foot, and variations in tuning prior to the setting of A = 440 Hz as standard pitch in the 20th Century.
Read more about this topic: Eight Foot Pitch