A closed and an open organ pipe have same lengths. If the ratio of frequencies of their seventh overtones is ( a a − 1 ) then the value of a is ________

Question

A closed and an open organ pipe have same lengths. If the ratio of frequencies of their seventh overtones is ( a a − 1 ​ ) then the value of a is ________

TestHub · Accepted Answer

For closed organ pipe f c ​ = ( 2 n + 1 ) 4 ℓ v ​ = 4 ℓ 15 v ​ For open organ pipe ​ f o ​ = ( n + 1 ) 2 ℓ v ​ = 2 ℓ 8 v ​ f o ​ f c ​ ​ = 16 15 ​ = a a − 1 ​ ⇒ a = 16 ​

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