An open vertical tube is filled with water and a tuning fork vibrates over the t

Question

An open vertical tube is filled with water and a tuning fork vibrates over the top near the open end. As the water level is lowered in the tube, the first resonance is heard when the water level is at 25 cm from the top of the tube.

http://imgur.com/gctaeqz

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

b) As we continue to lower the water level in the tube, the second f1 and the third f2 resonances are heard when the heights are h1 and h2 in the air column. What is the height h2? Answer in cm

Explanation / Answer

speed of sound is v = lamda*f

for first resonance L = lamda/4

lamda = 4*L = 4*0.25 = 1 m

then

frequency of the tuning fork is f = v/lamda = 343/1 = 343 Hz

for second resonance

h1 = 3*lamda/4 = 3/4 = 0.75 m = 75 cm

h2 =5*lamda/4 = 5*/4 = 1.25 m = 125 cm

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