In an organ pipe whose one end is at x = 0 , the pressure is expressed by p = p 0 cos 3 π x 2 sin 3 0 0 π t where x is in meter and t in seconds. The organ pipe can be

Step-by-step solution

For x = λ 3 π x 2 = 2 π ⇒ λ = 4 3 at x = 0 there is a pressure antinode. So first end must be close and in case of close at bot end l ⁡ = n λ 2 ⇒ l ⁡ = 2 n 3 for close at one end l ⁡ = 2 n + 1 λ 4 = 2 n + 1 3 So for close at one end possible lengths are 2 n + 1 3 = 1 3 , 1 , 5 3 , 7 3 Open at both ends is not possible for close at both end possible length are 2 n 3 = 2 3 , 4 3 , 2 , 8 3 ...... so only possibility is (3)