Question

On a day when the speed of sound is
345 m/s, the fundamental frequency of a closed organ pipe is
220 Hz. The second overtone of this pipe has the same
wave length as the third harmonic of an open pipe. How long
is the open pipe?​

Answer 1

Answer:

Let ll be the length of closed organ pipe and l′l′ be the length of open pipe .

wavelength of second overtone in closed pipe ,

λ=4l/5

λ=4l/5 ,

wavelength of third harmonic in open pipe ,

λ

′

=2l

′

/3

given λ=λ

′

λ=λ′ ,

or 4l/5=2l

′

/3

or l

′

=12l/10

now given, fundamental frequency of closed organ pipe , f=220Hzf=220Hz ,

we have f=v/4l

or l=v/4f=345/(4×220)=0.392m

therefore l

′

=12l/10=1.2×0.392=0.470m