Incorrect. In the figure, S is a small loudspeaker driven by an audio oscillator
ID: 2166873 • Letter: I
Question
Incorrect. In the figure, S is a small loudspeaker driven by an audio oscillator and amplifier, adjustable in frequency from 1500 to 2700 Hz only. Tube D is a piece of cylindrical sheet-metal pipe 54.1 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 1500 Hz to 2700 Hz? (b) What is the lowest resonant frequency in the given interval?Explanation / Answer
(a) Since the pipe is open at both ends there are displacement antinodes at both ends and an integer number of half-wavelengths fit into the length of the pipe. If L is the pipe length and is the wavelength then = 2L/n, where n is an integer. If v is the speed of sound then the resonant frequencies are given by f = v/= nv/2L. Now L= 0.541 m,so
f = n(344 m/s)/2(0.541 m) = 317.93n Hz
To find the resonant frequencies that lie between 1500 Hz and 2700 Hz, first set f = 1500 Hz and solve for n, then set f = 2700 Hz and again solve for n.
The results are 4.72 and 8.49, which imply that n = 5, 6, 7, and 8 are the appropriate values of n.
Thus, there are 4 frequencies.
(b) The lowest frequency at which resonance occurs is (n= 5) f= 5(317.93 Hz) = 1589.65 Hz.