Two pipes closed at one end, 51 cm and 52 cm long, produce 3 beats per second when they are sounded together in their fundamental modes. Ignoring the end correction, calculate the speed of sound in air.

Explanation

Data ` L_(1) = 0.51 m, L_(2) = 0.52 m` beat frequency = 3Hz
Since ` L_(1) lt L_(2) , n_(1) gt n_(2)`
Beat frequency = `n_(1) - n_(2) = 3Hz `
` n_(1) = v/(4L_(1)) and n_(2) = v/(4L_(2))`
` v/4 (1/L_(1) - 1/L_(2)) =3`
The speed of sound in air.
` v = (12L_(1)L_(2))/(L_(2)-L_(1)) = (12(0.51)(0.52))/(0.52 - 0.51) = 12 xx 51 xx 0.52 = 318 .3 ` m/s