MEASUREMENT OF THE SPEED OF SOUND IN AIR
Apparatus
1000 ml graduated cylinder, resonance tubes of various diameters, set of tuning forks in
the frequency range 256 Hz to 512 Hz, vernier callipers, metre stick, retort stand, clamp
and wooden block.
Procedure
4.
5.
6.
7.
1. Clamp the tube so that the water in the
graduated cylinder closes its lower end.
The tube should be free to slide
vertically through the clamp jaws.
2. Strike the highest frequency (512 Hz)
tuning fork on a wooden block, and hold
it in a horizontal position just above the
mouth of the tube with the length of the
being, l1, as small as possible (Fig. 1).
(thus ensuring first antinode and hence
fundamental frequency)
3. Slide the tube slowly up until the note
heard from the tube is at its loudest;
resonance is now occurring.
Tighten the clamp in this position and measure the length of the air column (from
the water level to the top of the tube) l1 with a metre stick.
Note results.
Calculate the speed of sound from c  f , for each of the tuning forks.
The antinode forms above the top of the tube and so an end correction factor has
to be added to the length. From theory, it is found that the correction factor is e =
0.3d , where d is the average internal diameter of the tube (measured using a
vernier callipers). (We get the diameter three times and get the average).
Hence λ = 4(l1 + 0.3d)
c = f
c = 4f(l1 + 0.3d).
8. Repeat for different resonance tubes of varying diameter
9. Get average value for speed of sound.
Precautions:


Ensure that the experiment starts at the smallest length and gets longer to
ensure that the fundamental frequency is gotten (sic)
Allow for the correction factor as mentioned in point 7 above.





Repeat the internal diameter three times in order to get an average.
Repeat the experiment a number of times with different resonance tubes in
order to get an average.
Measure lengths in mm in order to reduce length percentage error.
Avoid parallax errors when reading lengths.
Ensure that the vernier callipers is set to zero before use.
Results
f/Hz
l1/m
(l1 + 0.3d)/m
 = 4(l1 + 0.3d)/m
C = fλ / m s-1
The average value of the speed of sound in air =
Problematic Question 1:
If you do not get the fundamental frequency, then you can not use the formula
c = 4f(l1 + 0.3d).
Take this scenario, for example.
This is not the fundamental frequency, so l is not equal to ¼ λ
The length (we’ll call l2) is ¾ λ.
Hence λ = 4/3 l2
Hence c = fλ becomes
c = 4/3 f (l2 + 0.3d).
with correction
Problematic Question 2:
A tuning fork is set vibrating over a resonance tube which can be varied from 0 cm
to 110 cm in length. At what lengths would you expect to find the resonance if the
tuning fork has a frequency of 425Hz and the speed of sound is 340ms-1.
(12)
First Position:
c
=
fλ
L1
=
¼λ
meaning
4L1
=
λ
becomes
c
=
f (4L1)
=
0.2m
hence c
=
fλ
L1
=
c / 4f
L1
=
340 / 4(425)
and
Second Position:
c
=
fλ
L2
=
¾ λ
meaning
4/3 L2 =
λ
becomes
c
=
f (4/3L2)
=
0.6m
hence c
=
fλ
L2
=
3c / 4f
L1
=
(3)340 / 4(425)
and
Third Position:
c
=
fλ
L3
=
5/4 λ
meaning
4/5L3 =
λ
becomes
c
=
f (4/5 L3)
=
1m
hence c
=
fλ
L3
=
5c / 4f
L3
=
(5)340 / 4(425)
and
The above question should make you understand why pipes open at one end only have
odd harmonics.
If it doesn’t you will need to bring it to my attention.
At this stage, you should include diagrams of the three different pipes involved above.