A 44-cm-diameter water tank is filled with 35 cm of water. A 3.0-mm-diameter spi

Question

A 44-cm-diameter water tank is filled with 35 cm of water. A 3.0-mm-diameter spigot at the very bottom of the tank is opened and water begins to flow out. The water falls into a 2.0-cm-diameter, 70-cmtall glass cylinder. As the water falls and creates noise, resonance causes the column of air in the cylinder to produce a tone at the column's fundamental frequency. You can assume that the height of the water in the tank does not appreciably change in 4.0 s. What is the frequency when the cylinder has been filling for 4.0 s? Express your answer with the appropriate units. What is the rate at which the frequency is changing (Hz/s) when the cylinder has been filling for 4-0 s?

Explanation / Answer

Part A : What is the frequency when the cylinder has been filling?

we know that,   f = 1 / T

where, T = time taken for filled a cylinder = 4 sec

then, we get

f = 1 / (4 s)

f = 0.25 Hz

Part B : What is the rate ata which the frequency is changing (Hz/s) when the cylinder has been filling?

(df / dt) = (0.25 Hz) / (4 s)

(df / dt) = 0.0625 Hz/s

(df / dt) = 6.25 x 10-2 Hz/s

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