Open Air Column: Harmonic Frequencies and Wavelengths | Symbolic Physics (AP Free Response 1995B6)
Including a breakdown of how we come by the harmonic formulas and based on the first half of this AP problem from 1995. The other half is covered in another video.
1995B6. A hollow tube of length L open at both ends as shown, is held in midair. A tuning fork with a frequency f0 vibrates at one end of the tube and causes the air in the tube to vibrate at its fundamental frequency. Express your answers in terms of L and f0.
a. Determine the wavelength of the sound.
b. Determine the speed of sound in the air inside the tube.
c. Determine the next higher frequency at which this air column would resonate.
The tube is submerged in a large, graduated cylinder filled with water. The tube is slowly raised out of the water and the same tuning fork, vibrating with frequency fo, is held a fixed distance from the top of the tube.
d. Determine the height h of the tube above the water when the air column resonates for the first time. Express your answer in terms of L.
Here are some other problems these results would help with. Note that the speed of sound in Celsius temperature T is approximately v = (331 + 0.60 T) m/s
An organ pipe is 116cm long. Determine the fundamental and first three audible overtones if the pipe is (a) closed at one end, and (b) open at both ends.
If you were to build a pipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes required?
(a) Determine the length of an open organ pipe that emits middle C (262 Hz) when the temperature is 18°C. (b) What are the wavelength and frequency of the funda- mental standing wave in the tube? (c) What are l and f in the traveling sound wave produced in the outside air?
A pipe in air at 23.0°C is to be designed to produce two successive harmonics at 280 Hz and 320 Hz. How long must the pipe be, and is it open or closed?
(II) How many overtones are present within the audible range for a 2.18-m-long organ pipe at 20°C (a) if it is open, and (b) if it is closed?