1. The problem statement, all variables and given/known data
We place a speaker near the top of a drinking glass. The speaker emits sound waves with a frequency of 3.75 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 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
2. Relevant equations
fn = nv/4L
v=fλ
3. The attempt at a solution
The distance between a node and an antinode is wavelength/4, so I calculate wavelength via lambda=v/f, converting 3.75 kHz to 3750 Hz. This gives wavelength equal to 0.091466667m. I then take 14.1 cm, convert it to 0.141 m, and subtract the 0.091466667/4 from it to get the depth of the water, which is 0.118133333 m, or 11.8 cm. Which is wrong.
I next try 5λ/4 (using n=5) and get 0.027 m, or 2.7 cm which is also wrong, but 7λ/4 yields a negative answer, and 3λ/4 is gives an answer larger than 5λ/4
We place a speaker near the top of a drinking glass. The speaker emits sound waves with a frequency of 3.75 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 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
2. Relevant equations
fn = nv/4L
v=fλ
3. The attempt at a solution
The distance between a node and an antinode is wavelength/4, so I calculate wavelength via lambda=v/f, converting 3.75 kHz to 3750 Hz. This gives wavelength equal to 0.091466667m. I then take 14.1 cm, convert it to 0.141 m, and subtract the 0.091466667/4 from it to get the depth of the water, which is 0.118133333 m, or 11.8 cm. Which is wrong.
I next try 5λ/4 (using n=5) and get 0.027 m, or 2.7 cm which is also wrong, but 7λ/4 yields a negative answer, and 3λ/4 is gives an answer larger than 5λ/4
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