A narrow pipe is open ended and is placed next to a speaker in a room at 20 degr

Question

A narrow pipe is open ended and is placed next to a speaker in a room at 20 degree C. The signal source driving the speaker has adjustable frequency. However, like all such sources it only produces a clean signal over a limited frequency range. The column of air in the pipe is found to resonate at 90 Hz, 120 Hz, 150 Hz and 180 Hz, but not at any frequencies between these. Because of the limitations of the signal source it cannot be conclusively tested outside of this range. What other frequencies will this pipe resonate at? In particular, if we had a source that would produce a clean signal at low frequencies, what is the lowest frequency at which the pipe would resonate? Which harmonics of the pipe are 90 Hz, 120 Hz, 150 Hz and 180 Hz? How long is the pipe? If we seal one end of the pipe, what frequencies will it resonate at?

Explanation / Answer

1)210,240,270...
2) when f=90 is 343/90=3.8111

   when f=120 is 343/120=2.858333

   when f=180 is 343/180=1.9055

(n/2)=length of pipe...(1)

(n/2+0.5)2=(n/2)1=length of pipe

=)1+1/n=1/2

1+1/n=3.8111/2.8533=1.33

we get n=3

least freq wen n=1..=30Hz

b)3,4,5,6

c)from eqn 1..length=3.8111*3/2=5.7165

d)l=/4..for first harmonic

therefore..least f=343/4*5.7165=15hz

15,45,75,105

plss rate if it is helpful

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