Description

Speed of Sound
Objective: To measure the speed of sound in air at room temperature using
resonance in air columns.
Equipment: Resonance column apparatus, a set of tuning forks.
Reference: R.D. Knight, Physics for Scientists and Engineers, Ch.21 Superposition
Theory:
You will determine the speed of sound in air by measuring the
wavelength of a standing wave for a sound of known frequency. A standing
wave is what you get when two or more traveling waves combine in such a
way that there are s

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Speed of Sound
Objective:
To measure the speed of sound in air at room temperature using resonance in air columns.
Equipment:
Resonance column apparatus, a set of tuning forks.
Reference:
R.D. Knight,
Physics for Scientists and Engineers
, Ch.21 Superposition
Theory:
You will determine the speed of sound in air by measuring the wavelength of a standing wave for a sound of known frequency. A standing wave is what you get when two or more traveling waves combine in such a way that there are some places where there is no motion at all, and those places are called nodes. For any wave with wavelength λ (in m and frequency f (in vibrations!s, or !s, or #$, the speed of the wave (v, in m!s is%
λf
&
v
A sound wave is a traveling variation in air pressure, the air itself is not transported from one side of the room to the other. 'he speed it travels depends on the pressure, humidity and temperature of the air. #igh humidity, high temperature and high pressure all lead to a higher speed v. na tube, which is closed at one end and open at the other, you can get a standing sound wave set up in the tube with a displacement node at the closed end, and a displacement antinode at the open end. )ee pictures below. *hat that means is, the open end will be a place where the air vibrates most vigorously (a displacement antinode and at the closed end there will be a minimum amount of vibration (a displacement node.
For the +rst standing wave shown, notice that the wavelength is times the length of the portion of the tube containing air, so we-ve +t/ ! of a wavelength in the tube. f we now make the air column 0 times longer, we-ll be able to +t/ 1 of a wavelength in the tube. n general, we can capture !2 0!2 3!2 4 of the wavelength in the tube, by ad5usting the level of water to 5ust the right length. t all comes from insisting that there be a displacement antinode at the open end and a displacement node at the closed end. 6e7t, you should know about resonance. For e7ample% play a note A (8vibrations!s ne7t to a string whose length is such that one of its possible standing waves has this same frequency. 'hen the string will vibrate at 8 #$, even if you don-t pluck it. 'his is called resonance. )o, say you hold a tuning fork above a tube with one end open and the other end closed. f you ad5ust the length of the air column in the tube, and you +nd the shortest length at which the tube will resonate (you will be able to hear it, you will know that the length of the column is ! of the wavelength of the sound wave. 6ow keep making the column longer, and the ne7t time you hear resonance, your tube will have reached 0! of the wavelength. 'he ne7t resonance will be at a length of 3! the wavelength, and so on. f the
frequency is stamped on the tuning fork, then you will have frequency and wavelength, and you can multiply them together and +nd the speed of soundin air.A general e7pression for the speed of sound in a gas, from which we can derive the e7pression%where 9& ., : & ;0 <!(kmol=>, ' & temperature of the room during the e7periment in >, and ? & @;%; kg!kmol. 'hus, by measuring the temperatureof the room in
B and adding @C0 to convert it to >, you can make an independent estimate of what the speed of sound should be.
Activity:
As e7plained above, for a tone of wavelength λ, there can be a standing wavein an airD+lled cavity of length E closed at one end if%n reality it is not quite true. 'he top antinode is located slightly above (7 cmthe tube, so you have E
n
7 & n=λ!Gsing a glass tube +lled to a variable height with water, you will vary E until you +nd the place of resonance for various tuning forks of known frequencies, and thus +nd λ. 'he easiest way to do this is to +nd the distancebetween any two neighboring resonance points (which will be !@ of a wavelength, and multiply that by @ to get λ. n this case you will not need toknow the correction 7. ndeed, (E@ 7 H (E 7 & distance between any two neighboring resonance &0λ! D λ! & λ!@ 'he speed of sound can then be calculated by multiplying the wavelength λ by the frequency f stamped on the tuning fork. Io this three times, using a diJerent tuning fork and!or a diJerent pair of neighboring resonances each time. 'he highest and lowest values give you range D your e7periment predicts v to be within that range of values.
6ow measure the room temperature ' and convert it to >, and calculate the theoretical speed of sound v
theoretical
using equation above.Bheck to see whether the value you obtained for v
theoretical
falls within therange obtained for v
e7perimental
. n addition, you should compare your range of values for v
e7perimental
to that of at least one other lab group. You are both measuring the same thing at appro7imately the same time in appro7imately the same place, so your results should agree2 see if they do. 'ake care with the following%
ã
'ake your time and try to +nd the points of resonance as precisely as possible2 it-s not easy to +nd the e7act place. Knce you have found your +rst resonance point, try holding the tuning fork in diJerent orientations to +nd which one gives the best response, then +nd the resonance point again and start taking data.
ã
Ion-t knock the tuning forks against a hard surface D it dents them andthis might change their frequency slightly. #it them against piece of rubber.
ã
'he tubes are marked in cm. Bonvert your measurements to m, before doing any calculations, so that your +nal answer is in m!s.
What to Include in the Lab Report:
ã
Table with data
Numberf (Hz)L
1
(m)L
2
(m) (L
2
– L
1
) (m)1234
ã
!n this e periment f and #$
2
% $
1&
are 'our (ariables. )se e*uation ( + 2f#$
2
% $
1
& in the form ' + m b. !dentif' ', and b and write them down. Draw an appropriate graph and measure its slope. )se the slope to obtain a (alue for the (elocit' of sound in air at room temperature.
ã
Speed of sound in air is gi(en b' the e*uation
v RT M
=
where r is the gas constant, - is the molar mass of air and T is the Kel(in temperature. )se 'our measured (alue of speed of sound and the room temperature to obtain a (alue for the speed of sound in air at #a&
o
C, #b& at 1
o
C.
ã
)sing the relation
λ
+ (/f and using e*uation $
1
+
λ
/0, calculate 0 different (alues of , the end correction using the measured (alue of ( and the four fre*uencies of the tuning forks. lso obtain 0 (alues of using e*uation
ã
$
2
+
λ
/0. 3btain an a(erage (alue for .

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