Physics III (PHYS 2450L)
Week 7 - Standing Waves in a tube
Sound Waves
Sound waves are caused by mechanical oscillation pressure in medium. The propagation of sound waves
!
in air has a speed of approximately 331 " at 273 K which has the relation of velocity to frequency and
wavelength of,
𝑣 = 𝑓𝜆
(5)
Speed of sound in air at temperature T can be determined by,
𝑚
𝑇(𝐾)
𝑣! = $331.5 𝑠 % &273 (𝐾)
(6)
Sound waves that are traveling through an open-close air tube will undergo reflection upon the incident
end cap. The incident and reflected waves produce a resultant wave, similar to that of standing waves on
a string. The difference in the two adjacent anti-nodes of sound waves in such a tube or the difference
between two nodes is
∆𝐿 =
𝜆
2
(7)
Fig. 1. Standing waves in a closed-closed tube.
1
Fig. 2. Acoustic resonance in a closed tube
For a sound wave that is in a closed tube resonance can be determined with a microphone and
displayed on an oscilloscope. By adjusting a plunger in the tube, the resonant cavity length can be
altered. If resonance is detected at point, 𝑃- , at position 𝑥- , then if shifted through 𝑗./ number of
resonances to position 𝑥0 , the wavelength can be determined by,
𝜆=
2
0𝑥 − 𝑥- 2
𝑗 0
In other words, if the distance between 2 adjacent anti-nodes is ∆𝑥, then the wavelength is 2∆𝑥. If the
distance between the anti-node 1 to anti-node 3 is ∆𝑥1, then the wavelength =
1∆34
1
.
Fig. 2. Acoustic resonance experiment setup.
2
A. Acoustic Resonance
1.
2.
3.
4.
The acoustic system is set up as shown in figure above.
Initially position the plunger toward the speaker end of the system.
Turn on the frequency generator and set it to 1000 𝐻𝑧.
The wave from the generator and the sound wave from the microphone will be shown on the
oscilloscope.
5. Pull the plunger out until a resonance (peak amplitude) is observed on the screen. Record the
initial plunger position, 𝑥- , in Table 5.
6. Pull the plunger to the following resonance 𝑗 = 1 at position, 𝑥4 .
Record the positions up to 𝑗 = 3.
7. Using Eq. 8, Calculate the wavelength for each and take the average.
8. Repeat step for frequencies 1300 𝐻𝑧 and 1600 𝐻𝑧 .
9. Using the Average wavelengths calculate the speed of sound in air for each frequency and take
the average of all three.
10. Compare the calculated average speed of sound to the theoretical value (Eq. 6).
Acoustic Resonance
j
1000 𝐻𝑧
𝑥- (cm)
𝑥0 (cm)
Wavelength (cm)
Speed of sound (m/s)
1
2
3
1
1300 𝐻𝑧
2
3
1
1600 𝐻𝑧
2
3
Accepted
Speed of
Sound
Table 5.
Average
Speed of
Sound
Percent
Error
(%)
3