A simple apparatus for demonstrating resonance in an air column is depicted in t

Question

A simple apparatus for demonstrating resonance in an air column is depicted in the figure. A vertical pipe open at both ends is partially submerged in water, and a tuning fork vibrating at an unknown frequency is placed near the top of the pipe. The length L of the air column can be adjusted by moving the pipe vertically. The sound waves generated by the fork are reinforced when L corresponds to one of the resonance frequencies of the pipe. For a certain pipe, the smallest value of L for which a peak occurs in the sound intensity is 8.26 cm.

(A) What is the frequency of the tuning fork?

(B) What are the values of L for the next two resonance conditions?

In another similar setup, a tuning fork with unknown frequency is used, and the resonant positions are measured. However, the person taking the measurement lost the top of his page with the first few data. The only data left is the last two (consecutive) resonant positions recorded as 75.0 cm and 105.0 cm. From these data alone, what is the frequency of the tuning fork?

Explanation / Answer

given l1=0.75m and l2=1.05m

the unknown frequency is f= v / 2(l2-l1)

v=343 m/s velocity of sound

f=343/2(1.05-0.75)

f= 571.66 Hz------------Answer

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