We place a speaker near the top of a drinking glass. The speaker emits sound wav

Question

We place a speaker near the top of a drinking glass. The speaker emits sound waves with a frequency of 3.66 kHz. The glass is 14.1 cm deep. As I pour water into the glass, I find that at certain levels the sound is enhanced due to the 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 top of the glass. Assume that the antinode is exactly at the top of the glass. The speed of sound in air is 343 m/s. Give the answer to 2 significant figures.

Explanation / Answer

lamda=v/f=0.087(m)=8.7(cm). ---- for the excitation to occur. H=lamda*(k+1/2)/2=lamda*(k/2+1/4). where H is the distance from the water level to the top of the glass. with k = 0,1,2, 3,... H= 2.2(cm). 6.5cm 10.9 cm 15.2 cm. cause H max =14.1cm so with H=10.9, the depth of water is minimum. D=14.1-10.9=3.2(cm)

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