Question

two pipes closed at one end,53cm and 54cm long,produce 3 beats per sec when they are sounded together in their fundamental modes,ignoring end correction,calculate the speed of the sound in air​

Answer 1

Explanation:

Given Two pipes closed at one end,53 cm and 54 cm long,produce 3 beats per sec when they are sounded together in their fundamental modes,ignoring end correction,calculate the speed of the sound in air

• Let l be the length of pipe and v be the velocity of sound, then frequency of note emitted from the pipe is n = ν / 4 l
• Number of beats in 1 s = 3
• For a closed organ pipe  
• So x = n1 – n2
•        = ν / 4 (1 / l1 – 1/l2)
•      3 = ν / 4 (1/ 0.53 – 1 / 0.54)
•      3 = ν / 4 (1.886 – 1.851)
•      3 = ν / 4 x 0.035
•      Or ν = 12 / 0.14

   Or ν = 85.7 m / s

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