2. A common physics experiment involves lowering an open tube into a cylinder of water and moving the tube up and down to adjust the length of the air column in the tube. A tuning fork of frequency 330 Hz is sounded and held at the upper end as the tube is lifted out of the water until the first resonant sound is heard. The length of tube above the water level when the fundamental note sounds is 26 cm. a. Calculate the speed of sound in the air column in the tube. b. Determine another position for the tube that will result in a resonance with this tuning fork. c. Determine the first position (as we again lower the tube into the water) that will resonate with a 256 Hz tuning fork.

Question

Physics

Jefferson Neal

2 February, 17:41

2. A common physics experiment involves lowering an open tube into a cylinder of water and moving the tube up and down to adjust the length of the air column in the tube. A tuning fork of frequency 330 Hz is sounded and held at the upper end as the tube is lifted out of the water until the first resonant sound is heard. The length of tube above the water level when the fundamental note sounds is 26 cm. a. Calculate the speed of sound in the air column in the tube. b. Determine another position for the tube that will result in a resonance with this tuning fork. c. Determine the first position (as we again lower the tube into the water) that will resonate with a 256 Hz tuning fork.

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Angelica · Answer 1

This question pertains to resonance in air column. It is the case of closed air column in which fundamental note is formed at a length which is as follows

l = λ / 4 where l is length of tube and λ is wave length.

here l =.26 m

λ =.26 x 4 = 1.04 m

frequency of sound = 330 Hz

velocity of sound = frequency x wave length

= 330 x 1.04

= 343.2 m / s

b)

Next overtone will be produced at 3 times the length

so next length of air column = 3 x 26

= 78 cm

c)

If frequency of sound = 256 Hz

wavelength = velocity / frequency

= 343.2 / 256

= 1.34 m

= 134 cm

length of air column for resonance

= wavelength / 4

134/4

= 33.5 cm