PHYSICS LABS FOR SUBBU
strength
lab11.docLaboratory 11
Sound
Introduction
One aspect of superpositioning is that the amplitude of the resulting wave can be many times greater than that of the original waves. This can be a positive aspect, such as when an ampitheater is built to magnify the sound of performers on a stage without using electronic assistance (which can distort the quality of the sound). It can also have a negative aspect, such as when rouge waves are generated in the ocean that disrupt shipping.
Resonance occurs when the waves produced within a (semi-) closed region are reflected upon each other so that standing waves are produced. At the areas where the underlying waves constructively interfere with each other, the amplitude, and thus the intensity, or the standing wave is increased. In this lab, we will use the phenomenon of resonance to determine the speed of sound in the laboratory.
Additional background:
Imagine two waves of identical wavelength and amplitude traveling in opposite directions with equal speeds. The net displacement of the medium at any point and at any time is determined by applying the superposition principle, which states that the net displacement is given by the algebraic sum of the two individual displacements. The resulting wave pattern will then have points, separated by one-half wavelength, where the displacement is always zero. These points are called nodes. Midway between this nodes, the particles of the medium located at the antinodes, vibrate with maximum displacement.
We can visualize transverse standing waves on a string, of length L, fixed at both ends. These waves can be established by plucking the string at some point and are caused by continual reflection of the traveling waves at the boundaries, in this case the two fixed ends. The boundary conditions demand that at each end there must be a node. We can therefore fit an integral number of half-wavelengths into the length L of the string as shown in Fig. 1.
Even though the standing wave does not appear to be moving, we know that the waves underlying it move with a velocity, v, determined by the properties of the medium. The wavelengths of the traveling waves that combine to give the standing waves must fit within the overall length L such that the fixed ends correspond to nodes in the standing wave. Looking at Figure 1, we immediately see that
L=
nλ
n
2
where n is an integer that has values n = 1, 2, 3, …. Solving this for the wavelength shows that
λ
n
=
2L
n
,in other words, only certain wavelengths will result in a standing wave. Using the relationship v = f, where v is the speed of the underlying wave, the allowed frequencies are thus
f
n
=
v
λ
n
=
vn
2L
.Defining the fundamental frequency as
f
0
=
v
2L
,we can write
fn = nf0.
The frequencies are known as the resonance frequencies of the system. As can be seen from above, the lowest frequency of the system, having the longest wavelength, is called the fundamental frequency and the mode of vibration the fundamental mode or the first harmonic. The modes of vibration with progressively higher frequencies, are called second harmonic (n = 2), third harmonic (n = 3), etc. Notice that as the frequencies increase, the corresponding wavelength decreases, as expected.
Longitudinal waves can also be set up that create standing waves. The simplist way is to use a tube that is either open at only one end, or open at both ends. When the tube is open at one end, we refer to the tube as a closed air column. When it is open at both ends, the tube is an open air column.
Let's first consider a closed air column. In this case, the closed end of the pipe has to correspond to a node in the standing wave. The open end of the pipe will correspond to an anti-node. Graphically, this looks like
From the figure we see that the wavelengths have to satisfy
λ
n
=
4L
n
where n can only have odd values, n = 1, 3, 5, …. The corresponding resonant frequencies are then
f
n
=
nv
4L
=nf
0
where
f
0
=
v
4L
.If we look at an open air column, the situation is slightly different. Now we have anti-nodes at both ends of the pipe:
The resulting allowed wavelengths can be seen to still be
λ
n
=
4L
n
,with an associated frequency of
f
n
=
nv
4L
=nf
0
where f0 is the same as for a closed pipe. The only difference is that now, both even and odd values of n are allowed, n = 1, 2, 3, ….
The energy of the air at different locations along the sound wave are different. Uisng the following simulation examine what is happening to the molecules of air at the node and antinode:
http://www.walter-fendt.de/ph14e/stlwaves.htm
LAB Directions:
You will be given water, tubes or columns and tuning forks to examine the speed of sound and to investigate the relationships between frequency, speed of sound and wavelength. You will design your own lab with these materials and should consider the following questions to help you focus on a specific question and method of data collection.
Some questions that you should be considering as you develop your lab are:
Guided Inquiry Questions:
1) We know that the speed of sound varies with temperature as
v=v
0
√
T
T
0
, where v0 = 331 m/s, T0 = 273 K, and T is in degrees Kelvin. How can you determine this for the laboratory? Why do I want this value for the speed of sound?2) There is a frequency marked on the tine of the tuning fork. What does this correspond to? Do you need to assume any uncertainty in this value?
3) How can you measure the wavelengths of the various resonance positions for your closed pipe? What are the uncertainties in these measurements?
4) How can you determine which value for n corresponds to each resonance? Which resonances did you find?
5) What is the average speed of sound associated with each resonance position? What is the uncertainty associated with each of these averages?
6) Can you find a better estimate for the speed of sound from your different resonance averages? If so, how? What is the uncertainty associate with this estimate?
7) How accurate is your best estimate for the speed of sound? What are you using for the basis of comparison?
8) What would you get if you repeated this experiment using an open pipe?
Submit for Credit
· Include the full lab that provides the background/introduction section presenting information that is important in understanding the concepts.
· Be clear what your specific question(s) is(are) for your investigation.
· Provide a drawing, picture, image of your set up and a very clear description of how you collected data, measured data, calculated data.
· Provide a data table with the measurements you recorded. For example:
|
Frequency (f) |
n |
L(m) |
4L/n |
V=(4L/n)f |
T= 1/f |
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· Be sure to include an error analysis and explain the relevance of those errors to your results.
· Provide graphs that show relationships and patterns an ex[plain what the graphs show.
· Include a section that addresses the questions you asked (and most likely others from the guided questions above) and explain the meaning of the results, the lab and how it can be applied in a real world situation.
