Determine the greatest length of an organ pipe open at both ends such that its fundamental frequency lies within the normal hearing range ( 20 – 20 , 000 Hz ). The speed of sound in air is 340 m s ⁻¹ .

Step-by-step solution

The fundamental frequency of an organ pipe open at both ends is given by f = v 2L , where v is the speed of sound and L is the length of the pipe. For the length L to be maximum, the fundamental frequency f must be minimum. The minimum frequency in the normal hearing range is f_ min = 20 Hz . Substituting the given values, we get L_ max = v 2f_ min . L_ max = 340 2 20 = 340 40 = 8.5 m .