We place a speaker near the top of a drinking glass. The speakeremits sound wave

Question

We place a speaker near the top of a drinking glass. The speakeremits sound waves with

a frequency of 3.96 kHz. The glass is 14.1 cm deep. As I pour waterinto the

glass, I find that at certain levels the sound is enhanced due tothe excitation of standing

sound waves in the air inside the glass. Find the minimum depth(cm) of water at which

this occurs (distance from surface of water to bottom of glass).The standing sound wave

has a node at the surface of the water and an antinode at the topof the glass. Assume

that the antinode is exactly at the top of the glass. The speed ofsound in air is 343 m/s.

Give the answer to 2 significant figures.

Explanation / Answer

Given :          Freqency (n) = 3.96 x 103 Hz          Velocity of sound (v) = 343 m/s We know that :
wavelength of the wave is taking the glass as a closedtube(open at one end)          = v /n            = 343 / 3.96 x 103 Hz            = 0.0866m             = 0.0866 x 102 cm            = 8.66 cm For fundamental mode : We have :      L = /4         = 8.66 /4         = 2.165 cm minimum depth (cm) of water at which this occurs(distance from surface of water to bottom of glass).          x =(14.1 - 2.165) cm             = 11.935 cm           

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