A pipe open at both ends and a pipe closed at one end have same length. The ratio of frequencies of their P t h overtone is

Question

A pipe open at both ends and a pipe closed at one end have same length. The ratio of frequencies of their P t h overtone is, P + 1 2 p, p + 1 2 p + 1, 2 p + 1 2 p + 1, p 2 p + 1

MARKS App · Accepted Answer

Frequency of p th overtone of open organ pipe = p + 1 v 2 L …. (i) where, L = length of organ pipe and that of closed organ pipe is = 2 p + 1 = v 4 L …. (ii) So, the ratio of p th overtone of open to closed p + 1 v 2 L 2 p + 1 v 4 L (using Eqs. (i) and (ii)) = 2 p + 1 2 p + 1

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