Question

18. A pipe open at both the ends has a
fundamental frequency of 600 Hz. The
first overtone of a pipe closed at one
end has the same frequency as the first
overtone of the open pipe. How long are
the two pipes?​

Answer 1

A pipe open at both the ends has a fundamental frequency of 600 Hz the first overtone of a pipe closed at one end has the same frequency of the first overtone of the open pipe.

To find : The length of each organ pipe.

solution : fundamental frequency of open organ pipe, f = v/2l

where v is speed of sound i.e., v = 330 m/s

and l is the length of open organ pipe.

here f = 600 Hz

so, 600 = 330/2l

⇒l = 330/1200 m = 33000/1200 cm

⇒l = 330/12 = 27.5 cm

As it has given that first overtone of open organ pipe = first overtone of closed organ pipe

⇒2 v/2l = 3 v/4l'

⇒2 × 600 Hz = 3 × 330/2l'

⇒400 = 330/4l'

⇒l' = 330/1600 m = 33000/1600 cm

⇒l' = 20.62 cm