A closed and an open organ pipe have same lengths. If the ratio of frequencies of their seventh overtones is (a - 1)/a then the value of a i s _____.

Question

G1 Physics · Accepted Answer

For a closed organ pipe, only odd harmonics occur. Seventh overtone corresponds to 15th harmonic: f(closed) = 15v/(4ℓ) For an open organ pipe, seventh overtone corresponds to 8th harmonic: f(open) = 8v/(2ℓ) = 4v/ℓ Therefore: f(closed)/f(open) = [15v/(4ℓ)]/[4v/ℓ] = 15/16 Given: (a - 1)/a = 15/16 Therefore: a = 16