Question

Two organ pipe, open at both ends, are sounded together and 5 beats are heard per second. The length of shorter pipe is 0.25 m. Find the length of the other pipe. (Given: Velocity of sound in air = 350 m/s and end correction at one end = 0.015 m, same for both pipes.)

Answer 1

Given: l₁ = 0.25 m, v = 350 m/s, e = 0.015 m 

`n_1 - n_2=5`

`v/(2(l_1+2e))- v/(2(l_2+2_e)) = 5`

`v/2[1/(0.25+2xx0.015)+1/(l_2+2e)]=5`

`v[1/(0.25+0.030)+1/(l_2+2e)]=10`

`350 [1/0.280+1/(l_2+2e)]= 10`

`1/0.280 + 1/(l_2+2e)=1/35`

`1/0.280-1/35 = 1/(l_2+2e)`

`3.574-0.02857 = 1/(l_2+2e)`

`3.5424=1/(l_2+2e)`

`l_2 + 2e =0.2829`

`l_2 =0.0829-0.030`

`=0.2523  m`