An open vertical tube has water in it. A tuning fork vibrates over its mouth. As

Question

An open vertical tube has water in it. A
tuning fork vibrates over its mouth. As the
water level is lowered in the tube, a resonance
is heard when the water level is 62.5 cm below
the top of the tube, and again after the water
level is 87.5 cm below the top of the tube a
resonance is heard.

a. What is the frequency of the tuning fork?
The speed of sound in air is 343 m/s.
Answer in units of Hz

b. How many nodes are in the tube after the
water has reached the second distance from
the top of the tube?

Explanation / Answer

?/2 = l2-l1 = 87.5-62.5 = 50 cm = 0.5 m frequency = c/? = 343/0.5 = 686 Hz (b)length of nth overtone in a closed pipe = (2n+1)?/4 87.5 cm gives 3rd overtone so, there are 4 nodes.

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