In the figure below, S is a small loudspeaker driven by an audio oscillator with
ID: 1479269 • Letter: I
Question
In the figure below, S is a small loudspeaker driven by an audio oscillator with a frequency that is varied from 1000 Hz to 2000 Hz, and D is a cylindrical pipe with two open ends and a length of 62.0 cm.
(a) At how many frequencies does the sound from the loudspeaker set up resonance in the pipe?
_______________ frequencies
(b) What is the lowest frequency (of the given range) at which resonance occurs?
________________Hz
(c) What is the second lowest frequency (of the given range) at which resonance occurs?
_________________Hz
Explanation / Answer
a)
For pipe opened at both ends:
fn = n*V/2*L
speed of sound V = 343.2 m/s
fn = n*V/2*L
so,
fn = n*343.2 / 0.62
=n*553.55
so,
for n=2 and 3 f will lie between 1000 Hz and 2000 Hz
Answer: 2
b)
fn = n*553.55
if n=2
f2 = 2* 553.55 = 1107.1 Hz
Answer: 1107.1 Hz
c)
fn = n*553.55
if n=3
f2 = 3* 553.55 = 1660.6 Hz
Answer: 1660.6 Hz