A closed organ pipe and an open pipe of the same length produce 4 beats when they are set into vibrations simultaneously. If the length of each of them were twice their initial lengths, then find the number of beats produced.

Step-by-step solution

ν o p e n = V 2 L ν c l o s e d = V 4 L ⇒ ν o p e n - ν c l o s e d = 4 ∴ V 2 L - V 4 L = 4 ⇒ V = 16 L Now in 2 n d case:- ν ′ o p e n = V 4 L ν ′ c l o s e d = V 8 L ∴ ν ′ o p e n - ν ′ c l o s e d = V 8 L - V 4 L = V 8 L = 16 L 8 L = 2