350. assignment (fundamental frequency)

Standing Waves 

A hollow tube of length l, open at both ends as shown at right, is held in midair. A tuning fork with a frequency fo vibrates at one end of the tube and causes the air in the tube to vibrate at its fundamental frequency.

Express your answers to parts (a) — (c) in terms of l and fo.

(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.

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