Experiment 2: Velocity of Sound Laboratory Report Chelsea Leigh Tan, Kyle Gabriel Tanchuling, M a. Agatha Beatrice Uson, Angelica Uy, U y, Louise Erika Vargas Department of Math and Physics College of Science, University of Santo Tomas España, Manila Philippines
Abstract The speed of sound is simply its velocity which passes through an elastic mechanical medium (such of which are air, water, concrete, etc.). The speed of sound in a liquid medium is used for the measurement of speed itself. In the experiment, a medium filled with water was vibrated against a tuning fork. The tuning fork was used to get the vibration to obtain the speed of sound. The amount of water in the medium determines this speed, an increase or decrease in this will give a loud sound at some point. This sound indicates a resonance. The speed of sound from the experiment was then compared to
wavelength of sound can be determined through an air column's resonance. In this experiment, a long cylindrical plastic tube is used. This plastic tube is attached to a water reservoir. The volume of the water may be changed by lowering down, or raising the water level. While changing the water level, a tuning fork is then held over the open end of the cylindrical plastic tube. There is an indication of resonance when there is a sudden increase in the intensity of sound. In this experiment, students are expected to ❖
To verify the relationship between frequency of sound and its wavelength
❖
To determine the speed of sound by means of a resonating air column
❖
To determine the velocity of sound in a solid using a vibrating rod.
the actual speed of sound at 0 C which is °
331.4 m/s.
I. Introduction
Experiment 2 is all about the velocity of sound. The velocity of sound can be determined through the use of the equation: , where v = velocity of sound f = frequency λ = wavelength. wavelength. For this experiment, a tuning fork with a known frequency is used to determine the velocity of sound in air. On the other hand, the
=∙
II. Theory
A sound wave is a longitudinal and vibrational wave that travels through a medium, and oscillates along the direction of propagation. The speed or velocity velocit y of sound 1|GROUP 10
is dependent on how fast the energy of the vibration can be transferred across the medium. The wavelength and frequency of sound in a medium is related b y the formula:
= ∙
= 4( + 0.3)
where λ = wavelength of the sound produced
where v = velocity of sound propagation/ speed of sound in the medium f=frequency of the sound λ = wavelength of the sound in the medium The frequency can be computed by deriving the formula into:
=∙
The wavelength of sound produced in a resonance tube may be determined by this formula:
=
L = distance between the point of the loudest sound and the top of the glass tube D = diameter of the resonance tube 0.3 = constant Note that the L must be in meters as well as D. For solids, the speed of sound can be determined from the formula:
=
where VR = speed of sound in the solid
The same goes for determining the wavelength:
f = frequency of the sound wave
=
λR = wavelength of sound in the solid, which is also equal to twice the length of the solid
The speed is also dependent on the temperature of the medium. The formula for the speed of sound in air with a specific temperature is:
The theoretical speed of sound in a solution can be computed using the formula:
v = 331.4 m/s + 0.6t where v = velocity of the wave t = temperature of air in C °
331.4 m/s = speed of sound at 0˚C 0.6 = constant The formula shows that as the temperature increases, the speed of sound also increases.
= √ ρ where VR = speed of sound in the solid Y = Young's modulus ρ = density of the solid III. Methodology Activity 1: Resonating Air Column
2|GROUP 10
Start with the water near the top of the resonance tube apparatus. Strike a tuning fork with the rubber mallet. Place the vibrating tuning fork over the top of the glass tube. Lower the water vessel slowly until you hear the loudest sound. Mark the point where you hear the sound. Be sure that the fork is vibrating as you lower the vessel. If not, strike the fork again. Measure the distance between this point and the top of the glass tube. Record this as L. Don’t forget to convert this distance to meters. Measure the diameter (D) of the resonance tube. Compute the wavelength of sound produced Make two more trials and determine the average wavelength Using the average wavelength and the frequency engraved in the tuning fork. Compute for the velocity of sound in the air inside the glass tube using the formula. Velocity = frequency x wavelength. Determine the temperature in degrees Celsius of air inside the glass tube. Be sure that the thermometer is not touching the water. Compute the speed of sound in air at that temperature. Compare the speed in step 10 with the speed in step 8 by computing the % error. Use the speed obtained in step 10 as the accepted value. Repeat the procedure for the other tuning forks. Record your data and observations in the Data and Results table in the succeeding page. Activity 2: Speed of Sound (from Physics with Computers)
near the open end of a closed tube. Open the file “24 Speed of Sound” in Physics with Computer file. As soon as data collection begins, snap your fingers or clap your hands near the tube. From the graph that you will see on your computer screen, determine the time interval between the start of the first vibration and the start of the echo vibration. Note that this time interval is the time for sound to travel through the tube and back. Compute for the speed of sound by dividing the length of the tube by ½ of the time interval obtained in step 5. Compute for the % error with the same accepted value used in activity 1. Activity 3: Speed of Sound in Solid
Place a thin layer of cork dust as uniformly as possible inside the Kundt’s tube. Clamp the rod at its center. Rub the rod with a piece of cloth with coarse powder. This will set the rod into vibration producing sound of high frequency. A standing wave pattern will be formed in the cork dust inside the glass tube. Measure the distances between two consecutive displacement nodes. Get the average of these distances. Determine the frequency of sound produced. Using this frequency, determine the speed of sound (VR) in the rod. Compute for the theoretical speed of sound in the rod. Compute for the % Error. IV. Results and Discussion Activity 1:
Connect Vernier microphone to Channel 1 of the interface. Position this microphone
Temperature of Air = 250 3|GROUP 10
Diameter of Resonance Tube
A large percentage error was obtained. The error was caused by the following: 1) intensity of striking the tuning fork, 2) the observers’ lack of concentration, 3) and maybe the medium itself.
at 320Hz = 0.040m at 512Hz = 0.048m. Table 1. Wavelengths of tuning fork(s)
Frequency
Activity 2:
Wavelength (m)
of tuning fork
Trial 1
Trial 2
Trial 3
512Hz
0.3384m
0.3504m
0.3424m
320Hz
0.552m
0.472m
0.532m
Length of tube = 0.45m Table 2. Total travel time of sound wave
Trial
Total travel time
1
0.00235s
2
0.00268s
Average
2.52x10-3s
Experimental speed
357.14m/s
Theoretical speed
346m/s
% error
3.22%
Table 1.1. Cont. of Table 1
Average wave-
Experiment
Theoretic
%
length
al Speed
al Speed
error
0.3437m
175.97m/s
326m/s
46.02%
0.5187m
165.98m/s
326m/s
49.08%
Frequency of sound and wavelength are inversely proportional. If the frequency increases, the shorter the wavelength and vice versa. However, the speed of sound is not dependent on the frequency or the wavelength. The speed of sound depends on the properties of the medium, amplitude for example. The temperature also affects the speed of sound, giving the direct proportionality of the two properties of waves. Molecules having a higher temperature travel faster in a medium. Thus, this gives them the ability to move quickly in the medium; a higher velocity than in liquid or gas phase. In the graph given above, the relationship of the frequency and wavelength in the medium follows the theory of sound waves.
As discussed earlier, the speed of sound only depends on the medium and its properties. One thing that can only change the speed of sound is by changing the medium itself. One property of a medium is amplitude. Speed of sound is also determined by the square root of compressibility modulus, in Pascal (Pa). Activity 3:
# of nodes = 10 Table 3. Speed of sound in solid
Average of distances between node to node Wavelength of sound in air Frequency of sound
1.911m
3.8m 8664.92Hz
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Length of rod Wavelength of sound in rod Experimental speed of sound in the rod Theoretical speed of sound in the rod % error
1.122m 0.0382m 331.17m/s 331.00m/s 0.0513%
Speed of a sound is most likely to be fastest in a solid material. For liquid, it is faster than the speed of sound in gases. The molecules that make up the space of the solid is very intact, allowing the sound to travel faster in a solid medium. The velocity of sound is defined with two properties: density and elasticity. V. Conclusion
This experiment shows that the velocity of sound in the air can be found by using tuning forks of knowns frequency, and that the air column’s resonance can determine the wavelength of the sound. In the experiment, we concluded that the frequency of sound is inversely proportional to that of its wavelength, we also used the resonating air column to determine the speed of sound, and finally we used a vibrating rod to determine the velocity of sound in a solid. VI. Applications 1. What is the relation between frequency and wavelength of sound produced in a medium? - The relationship of frequency and wavelength are inversely proportional, they are related to velocity of a sound wave with the formula:
= ∙ So if the velocity is constant (sound is constant in a medium of constant density) then as the frequency increases, wavelength will decrease and vice versa. 2. What is the use of water in activity 1. - A closed end tube would resonate if its length is 1/4 the wavelength of the sound. If its length is 3/4, 5/4, and 7/4 wavelength long it could also resonate. Increasing the length of a vibrational system (the air inside the tube) would result in an increase in the wavelength and a decrease in the natural frequency of the system.
On the other hand, if the length of the vibrational system is decreased, the wavelength decreases and the natural frequency increases. This only means that changing the water level in the tube would result to the matching of the natural frequency of the air in the tube and frequency where the tuning fork vibrates. When this matching is achieved, the tuning fork forces the air column in the tube to vibrate at its own natural frequency. This results to a resonance which is always a big vibration (loud sound). To sum everything up, the water serves a medium where the vibration (sound) travels. 3. In medical practice, ultrasound in the range of 1 to 5 megahertz is being used as an imaging modality. The associated 5|GROUP 10
wavelengths in a typical human tissue range from 0.3mm to 0.06mm. Find the velocity of ultrasound in the tissue. - By using the fomula , the velocity of ultrasound could be computed.
= ∙ = (1+2 5) ∙ (0.3 +20.06) = 3∙ 0.18 = 0.52 /
4. The outer ear of a human may be thought of as a closed pipe 2.7 cm long on the average. What frequency would be most effectively detected by the ear
6. If you were lying on the ground, would you hear footsteps sooner or later with your ear touching the ground or not? - You would hear the footsteps sooner with your ear touching the ground. The reason behind this is solids conducts better than air. References
[1] http://www.csun.edu/scied/1-demo/reson ance_tube/resonance_tube.htm (retrieved on September 21, 2017) [2] http://www.physicsclassroom.com/class/ sound/Lesson-5/Resonance (retrieved on September 21, 2017)
at 30 C.
-
1.67 frequency.
5. Suppose that we increase the temperature of the air through which a sound wave is traveling. A) what effect does this have on the velocity of the wave? Explain B) for a given frequency, what effect does increasing the temperature have on the wavelength of the sound wave? Explain. - An increase in the temperature of the air give an increase in velocity of the sound waves. Since warmer air has a higher average velocity, increase in temperature would allow the air to transfer the energy more rapidly.
-
Since the velocity is equal to the product of the wavelength and frequency, an increase in the temperature would increase the wavelength since the frequency is the same. 6|GROUP 10
