In Fig. 17-40, S is a small loudspeaker driven by an audio oscillator and amplif
ID: 2203800 • Letter: I
Question
In Fig. 17-40, S is a small loudspeaker driven by an audio oscillator and amplifier, adjustable in frequency from 810 to 2800 Hz only. Tube D is a piece of cylindrical sheet-metal pipe 36.5 cm long and open at both ends. (a) If the speed of sound in air is 344 m/s at the existing temperature, at how many frequencies will a resonance occur in the pipe when the frequency emitted by the speaker is varied from 810 Hz to 2800 Hz? (b) What is the lowest resonant frequency in the given interval?
In Fig. 17-40, S is a small loudspeaker driven by an audio oscillator and amplifier, adjustable in frequency from 810 to 2800 Hz only. Tube D is a piece of cylindrical sheet-metal pipe 36.5 cm long and open at both ends. (a) If the speed of sound in air is 344 m/s at the existing temperature, at how many frequencies will a resonance occur in the pipe when the frequency emitted by the speaker is varied from 810 Hz to 2800 Hz? (b) What is the lowest resonant frequency in the given interval?Explanation / Answer
the resonant frequencies for such a tube is given by-
f = nv/2L n=1,2,3,........... and L is the length of the tube
or, f = 471.233n
So n can can maximum go to---
[2800/471.233] = 5.94.....so n can take maximum 5...
and minimum.....[810/471.233] = 1.71......i.e 2
So there are 4 resonant frequancies.....
lowest resonant frequency = 2*344/2*0.365 = 952.466Hz..