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 31 cm from the top of the tube.What is the frequency of the tuning fork? The speed of sound in air is 343 m/s. Answer in units of Hz. (part 2 of 2)As we continue to lower the water level in the tube, the second f1 and the third f2 reso- nances are heard when the heights are h1 and h2 in the air column. What is the height h2 ? Answer in units of cm.

Explanation / Answer

as given in the problem this is closed pipe so the harmonics are

first harmonic , resonance length h1 = 1*lambda /4 , second resonant length h2 = 3*lambda /4,

third resonant length h3 = 5*lambda /4

given speed of sound v = 343 m/s, and given h1 = 31 cm now lambda = 4*h1 = 4*31*10^-2 = 1.24 m

now V = lambda*f ==> f = V/ lambda = 343/1.24 = 276.6 Hz

for second resonance h2 = 3*1.24/4= 0.93 cm,

for third resonance lenght is 5 h1 = 5*31 = 155 cm

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