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 180 cm below the top of the tube, and again after the water level is 220 cm below the top of the tube a resonance is heard. what is the frequency of the tuning fork? the speed of sound in air is 343 m/s. answer in units

Answer 1

Since any first distanced1=λ(2N1−1)/4, whereN1= 1,2,3,· · ·will do, the first distance only cannot be used to know the wavelength.The space between the resonances is ½ a wavelength, soλ= 2 [d2−d1]= 2 [(35 cm)−(25 cm)]= 20 cm.
The frequency isF = vλ=343 m/s2 [(35 cm)−(25 cm)]= 1715 Hz.