6. Experiments to
measure the speed of sound in air and a solid
(a)
Using synchronised microphones to measure the
speed of sound in air
The experiment is performed by connecting a loud speaker to a
signal generator to generate the sound to be picked up by the microphones.
You select a particular known specific frequency e.g. 250 Hz (f in Hz).
Two microphones are connected to an
oscilloscope which pick up
the sound from the speaker and which is converted to an electrical signal by the
microphone and displayed as a trace on the cathode ray oscilloscope screen.
You can secure the speaker and two microphones with stands and
clamps making sure they are aligned at the same height.
You set up the oscilloscope to detect the sound wave signals
from both microphones - to give you two traces on the screen.
You start with the two microphones next
to each other near the speaker.
You then slowly move one microphone away from the other.
When the two microphones are first exactly one wavelength
apart, the two signal traces on the oscilloscope are exactly aligned -
synchronised, as in the diagram above.
The trace from the microphone 2, furthest
away from the speaker, will show a smaller amplitude - the diagram does not
take this into account!
You then measure the distance between the microphones and this
gives you the wavelength of the sound.
This is because the sound waves are aligned
in phase and
just one wavelength apart.
speed of sound wave (m/s)
= frequency of sound (Hz) x wavelength of sound wave
(m)
in 'shorthand'
v = f x
λ
you know the frequency in Hz from the
signal generator setting
and the wavelength is the distance
between the microphones in cm ==> m
You repeat the experiment to calculate the
average wavelength to give statistically the best result.
You can then repeat the experiments with
other frequencies from the signal generator and you should find the speed stays
the same, but, as the frequency is increased the wavelength of the sound wave
should get shorter.
(b)
Echo method to measure the speed of
sound in air
You need two people to do the experiment.
Measure a distance d, e.g. 50 m from a tall
wall or a building with a broad flat wall that will act as a sound wave
reflector.
You then clap two pieces of flat wood
together and adjust the rate of clapping until the sound of the claps are
synchronised with the return of the echo.
Use a stopwatch to find the time interval
between the claps e.g. measure the time of 10 claps and compute average.
Calculation of speed of sound in air.
If d = distance to wall (m), if
t = average time
interval between claps (s)
v = 2d/t (m/s)
Note that the distance is doubled because
the sound is 'going there and back' in the time interval t.
This is not an accurate method, the
clapping can't be done in perfect harmony, but its a bit of fun doing
it.
Example of speed of sound
calculation based on an echo
Suppose two students measured the
following data.
The side of the school sports
hall was 80 m away from the clapper.
50 claps took a total time of
24.2 s
v = 2d/t (m/s),
d = 2 x 80 = 160 m, average clap time = 24.2 / 50 = 0.485 s
speed of sound
v = 160 / 0.485 =
330 m/s (3 sf)
(c)
An experiment to measure the speed of sound in air using a stretched string or
wire.
In this method you use a mechanical
vibrator (vibration transducer) to vibrates a tensioned (stretched) steel
wire or elastic cord.
The vibrator, whose frequency is
controlled by the signal generator, continuously transfers energy to the
wire/cord making it vibrate.
This sends transverse waves down the
wire/cord and produces a particular note when the wire/cord vibrates with
specific number of wavelengths along the length of the wire.
The experimental set-up is shown below.
The wire/cord is fixed to the vibration
transducer and stretched horizontally over a pulley and tensioned with
weights on the end.
You switch on the signal generator and
observe the vibrations in terms of numbers of wavelength as you slowly
increase the frequency.
You note the frequency when the
vibrations seem 'stable' and a number of wavelengths can be clearly
observed from the stable wave 'pattern'.
You count the number of waves along
the wire/cord and the frequency displayed on the signal generator.
Things are a bit blurred so you need
to take care in your observations and note that when stable, the wire
seems to vibrate up and down and there seems to be points on the
wire which don't seem to move up and down (these points are called nodes
where the amplitude is at a minimum amplitude).
e.g. from the diagram 3 wavelengths = 60 cm, one wavelength =
20 cm or 0.20 m at a frequency of 1650 Hz.
speed = wavelength x frequency
speed of sound in air = 0.20 x 1650 =
330 m/s
You can repeat the experiments with
different frequencies to produce ½, 1, 1½, 2, 2½, 3, 3½, 4 etc. wavelengths
as you increase the frequency from the signal generator.
You can measure the number of wavelengths for
each frequency, and you should get the same speed of sound in air, even
though the note you hear changes.
You can experiment with different
'string' materials and different tension weights on the end of the wire.
You can also employ a bridge ↑ over which
the wire is stretched, so you can vary the length of the vibrating wire.
A simple home experiment to show a
standing wave in an elastic cord
I stretch a 30 cm (0.30 m) thick rubber
band above a wooden base and clamped it in position on wooden blocks (upper
photographs) and illuminated with a couple of suspended LED torches.
You can see, in the lower photographs,
the two extremes (maximum amplitude) the rubber band reaches when
tugged back and released to vibrate at its fundamental frequency.
The sound produced was rather 'dull', but
using the speed of sound (v)
as 330 m/s, you can
calculate the frequency of oscillation of the rubber band.
The wavelength (λ)
= 2 x 0.30 = 0.60 m
This is elastic cord length is
doubled because the half-wave doubles back on itself to give a
complete wavelength of the standing wave - the natural wavelength
and frequency resulting from the particular mass, length and tension
of the elastic cord (see animation below).
v = f x
λ, f = v / λ
= 330 / 0.60 =
550 Hz (hence the blurred photograph).
This calculation oversimplifies the situation, but it is correct in
principle! The note was not clearly heard, but on
stretching the same elastic band over an empty circular tin can of ~30 cm
diameter, with a similar tension, a note could be clearly heard!
The note was theoretically between
C5 and D5 on the musical frequency scale.
Standing waves are
illustrated by the wave 'pictures on the left'.
They correspond in length to
½, 1, 1½, 2, 2½ and 3
wavelengths.
The animation is from
https://en.wikipedia.org/wiki/String_vibration
(d)
A simple
experiment to measure the speed of sound in a solid
Introduction to the experiment
You can measure the speed of sound
waves in a solid by measuring the frequency of sound waves produced when
you hit a solid.
The method works best by hitting
metal rods that will resonate strongly, mainly with one particular
'note' called the fundamental natural frequency - think of a tuning fork
or musical triangle in music.
When you hit the rod, longitudinal
sound waves are induced in the metal and they will also vibrate
the surrounding air.
These sound wave frequencies can be
picked up by a microphone and displayed on the screen of an
oscilloscope.
You can pick out this fundamental
natural frequency from other frequencies because it should give the
highest amplitude signal.
The experimental set-up
A uniform rod of metal of known
length is suspended from its mid-point in a
horizontal position.
The rod (length L) needs to at least 50 cm long and a few cm in
diameter made of e.g. aluminium, brass or iron.
Near one end of the rod is placed a microphone connected
to an oscilloscope and a hammer at the ready!
The oscilloscope is used to monitor both the amplitude and frequency of the
sound waves produced when the rod is hit with the hammer.
Experimental procedure
This is a very technical experiment
to do!
The rod is hit at one end with the
hammer so it vibrates continuously making sound.
Tune in the oscilloscope to the
frequency range of greatest amplitudes.
Record the frequency as best you can
that corresponds to the highest amplitude on the screen.
Repeat several times to get the
average frequency - the best value you can obtain.
A bit of theory before the speed
calculation
When the rod is hit, its vibrations
produce lots of difference frequencies.
However, all objects have a natural
vibrational frequency that sets up a longitudinal standing wave
that should give the maximum amplitude of sound.
This particular frequency is
called the fundamental mode of vibration.
A standing wave does not vary its
amplitude profile i.e. it doesn't appear to move - stationary.
What you see is one wave
occupying twice the length of the rod.
I've shown this on the diagram in
the cyan inset box below the rod.
The wavelength of this fundamental
standing wave is equal to double the length of the rod.
(A point where the amplitude is zero
is called a node - don't need to know this point for GCSE physics.)
An example of calculating the speed
of sound in the rod
Suppose the rod is made of aluminium,
diameter 2 cm and length 65 cm.
If the maximum amplitude was found to
be at ~4.0 kHz, calculate the speed of sound in aluminium.
wavelength = 2 x L = 65 x 2 = 130 cm
= 1.3 m
frequency = 4.0 kHz = 4000 Hz.
speed = frequency x wavelength = 4000
x 1.3 = ~5200 m/s
Note that the speed of sound in
solids is much greater than in gases like air (~340 m/s).
INDEX of physics notes
on SOUND
Keywords, phrases and learning objectives for
sound waves
Be able to interpret, describe or explain experiments to measure
the speed of sound in air or
solid.
Know the use of synchronised microphones, echo timing, tensioned wire-standing
wave methods to measure the speed of sound in the school laboratory
- the apparatus and lab procedure and any calculations based on
observations-data.
Use your
mobile phone in 'landscape'?
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