The fundamental frequency of a closed pipe is 400 Hz . If ( 1 3 )^ rd length of the pipe is filled with water, the frequency of the 2^ nd harmonic of the pipe will be (Neglect end correction)

Step-by-step solution

The fundamental frequency of a closed pipe is given by f₁ = v 4L , where v is the speed of sound and L is the pipe length. Given f₁ = 400 Hz, we have v 4L = 400 Hz. When 1 3 of the pipe is filled with water, the effective air column length becomes L' = 2 3 L . The new fundamental frequency is f₁' = v 4L' = v 4( 2 3 L) = 3v 8L . Substituting v 4L = 400 Hz into the expression for f₁' yields f₁' = 3 2 (400) = 600 Hz. For a closed pipe, the harmonic frequencies are the odd multiples of the fundamental frequency. The se