Two open pipes both have length L 50 cm but one has diamete

Two open pipes both have length L = 50 cm, but one has diameter D1 = 10 cm and the other D2 = 2 cm. What is the maximum number of harmonics that could possibly be strong in the spectrum of each?

Solution

End correction for open organ pipes is 0.6D

So, for pipe 1 with D1=10cm end correction=6cm

& for pipe 2 with D2=2cm end correction=1.2cm

Effective length of organ pipe 1&2=> 44cm, 48.8 cm

For nth harmonic =2*L_eff/n

For both having same frequency, ratio of harmonics=110/122

There will be infinitely many harmonics that will be strong in the spectrum of each as all the overtones will be strong, theoretically speaking.