Almost the entire length of an aluminum pipe of length 1.1m is dipped vertically in water contained in a tall jar. An excited tuning fork of frequency 500 Hz is held at the upper end of the pipe and the pipe is gradually raised. How many discrete resonance conditions are possible? (Speed of sound in air = 330 m/s)

The arrangement mentioned in this problem makes a simple resonance column apparatus. The wave length of sound emitted by the fork, λ = v/n = 330/500 = 0.6666 m. The first resonance (fundamental mode) is obtained when the exposed length of the pipe is λ/4. The second resonance is obtained when the exposed length is 3 λ/4. These two are definitely possible since the length of the pipe is 1.1 m and λ = 0.6666 m. The third resonance will be obtained when the exposed length is 5λ/4 = 5×0.6666/4 = 0.83 m. This too is possible. The fourth resonance will be obtained when the exposed length of the pipe is 7λ/4 = 7 × 0.6666/4 = 1.16 m. This is not possible since the length of the entire pipe is 1.1 m only.