Closed Air Column of Varying Length: Resonant Frequencies | Symbolic Physics (AP FR 1995B6)
This can be seen as a continuation of the open-column case: • Open Air Column: Harmonic Frequencies and ...
There we presented the AP problem this one is based upon.
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 problems that these results are helpful for:
B2004B3. A vibrating tuning fork is held above a column of air, as shown in the diagrams above. The reservoir is raised and lowered to change the water level, and thus the length of the column of air. The shortest length of air column that produces a resonance is L1 = 0.25 m, and the next resonance is heard when the air column is L2 = 0.80 m long. The speed of sound in air at 20° C is 343 m/s and the speed of sound in water is 1490 m/s.
(a) Calculate the wavelength of the standing sound wave produced by this tuning fork.
(b) Calculate the frequency of the tuning fork that produces the standing wave, assuming the air is at 20° C.
(c) Calculate the wavelength of the sound waves produced by this tuning fork in the water, given that the frequency
in the water is the same as the frequency in air.
(d) The water level is lowered again until a third resonance is heard. Calculate the length L3 of the air column that
produces this third resonance.
(e) The student performing this experiment determines that the temperature of the room is actually slightly higher
than 20° C. Is the calculation of the frequency in part (b) too high, too low, or still correct?
A pipe that is closed at one end and open at the other resonates at a fundamental frequency of 240 Hz. The next lowest/highest frequency it resonates at is most nearly:
A) 80 Hz B) 120 Hz C) 480 Hz D) 720 Hz
A tuning fork is set into vibration above a vertical open tube filled with water. The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125m and again at 0.395m. What is the frequency of the tuning fork?
A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closed pipe. (b) What is the fundamental frequency of this pipe?
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?