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Experiment ( 2)
MEASURING THE SPEED OF SOUND IN AIR -
DETECTING DOPPLER EFFECT
2.1
Introduction
We encounter sound waves on a daily basis. Sound Waves arelongitudinal mechanical waves that require an elastic media for
propagation. If it weren't for sound waves, many species including
human beings wouldn't have survived. Sound waves have constantvelocity as long as they dont encounter different media or different
conditions (e.g. different temperatures) that is independent of
the wavelength and frequency of the waves, otherwise you could have
heard a different orchestra symphony from the one seating behind or in
front you in Opera house. Thus, the velocity can be determinedby measuring the travelling time through a well known distance.
Another distinct phenomenon concerns sound waves is Doppler
Effect, when wavelength, and consequently frequency, changes due tothe movement of the sound source, the listener or both relative to the
propagation media. Due to reduction or increase of the spacing
between two successive wave fronts as the source or the listener move,
the sound of approaching car is different from the sound of a recedingone.
2.2
Objectives
Determination of the speed of sound in air by measurement
of sound travel times across known distances.
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Investigation of the Doppler Effect (The shift of the detected
frequency as the relative velocity between the source and the
detector is varied).
2.3
Theory
Sound waves consist of a series of compressions and rarefactionswhich established by the particles of the medium. They are a
longitudinal waves in which the particles oscillate back and forth
along the direction of propagation and can propagate through anymedium, gas, liquid, or solid. The human ears are sensitive to sound
waves of frequency range 20 Hz up to 20,000 Hz. Ultrasonic waves
are sound waves of frequencies above 20,000Hz while infrasonic arethose below 20 Hz.
2.3.1 Speed of sound in media
The speed of sound is variable and depends on the properties of
the substance through which the wave is travelling. In ideal gases
and air it can be proven the t the velocity of sound is given by,
where, = is the ratio of heat capacities of the gas, R is thegas constant which is equal for all gases= 8.3144 J/mol.K, T is the
absolute temperature in kelvins and M is the molar molar mass(mass
per mole) of the gas. For air,
= 1.4 = 28.8 10/and at = 20 = 293 , we find = 344 /
Many methods are used to determine the velocity vof sound in
air. One of the simplest method is to measure the time period twhich
a sound pulse takes to travel a distance din the medium, where,
= ( 2.1)
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Since the distance dis usually small, the propagation time periodt is extremely small and a measuring device of resolution 106 s
should be used.
2.3.2 Doppler Effect in waves
One of the most important phenomena in waves is the DopplerEffect. Consider a source S of sound standing at certain distance
from a detector D and emitting sound waves of certain tune
frequency fo . As there is no relative motion between the soundsource and the detector, it always detects the sound with the same
tune frequency fo. Now, if the sound source is approaching the
detector, it detects the sound with higher frequency than the source
frequency, while, if the source moves away from the detector, itappeared to have lower frequency than the source. This effect is
known as the Doppler effect in which waves are shifted from its
original frequency to lower (if the source is far away) or higher (if
the source is approaching).
It is found that the relation between the source frequencyfoand
the detected frequencyfd is given by,
Where vis the velocity of sound in air (independent on source
and detector), vsis the source velocity and vdis the detector velocity
(both with respect to air). These velocities are in the same direction
and along the line joining them, as shown in Figure 2.1.
vd vs
D S
Figure 2.1: The postive directions of source and detector velocities.
= ( 2.2)
= + + ( 2.3)
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In this experiment, we examine the following cases:
a.
The source approaching the standing detector.In this case vd =0 and vs is in the negative direction and fd fo,
where,
b. The source is moving away from the standing detector.
In this case vd =0 and vs is in the positive direction and fd fo,
where,
c. The detector approaching the standing source.
In this case vs =0 and vd is in the positive direction and fd fo,
where,
d.
The detector is moving away from the standing source.In this case vs=0 and vdis in the negative direction andfd fo,
where,
= || ( 2.4)
= + ( 2.5)
= +
( 2.6)
= || ( 2.7)
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2.4
Task1: Determining the speed of sound in air
2.4.1
Setup
Figure 2.2. shows the setup used to measure the velocity of sound in
air. Polyuretheen foam is used to cover the back and the side barriers
of the bench to reduce noise that may affect the microphone. Also,
put the barrel bases which are carrying the microphone and the rod
on a piece of the foam.
Figure 2.2: The setup used for measuring the speed of sound in air
1 Universal Counter 4 Support, 100 mm
2 Microphone with amplifier 5 Barrel base
3 Support rod with hole, 100 mm 6 Measuring tape, 2 m
2.4.2 Procedure
1- Use the setup shown in Figure 2.2. One of the barrel bases
should either stand on foamed material or be set up on a
different table top to avoid measuring sound velocity of sound
travels through the bench.
2- Check the wiring as shown in Figure 2.3.
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Figure 2.3: The electric wiring of the setup
3- Connect the right clamped support (4) and the clamped rod (3)
to the to the Stop and
Ground jacks of Gate 1.
4- Connect the microphone
amplifier to the Stop and
Ground jacks of Gate 2.
5- In the universal counter,
use the function Timer
then set the Trigger to
two incoming pulses
as shown in Figure 2.4
6- Use the measuring tape to
set the distance between
the right support and the
microphone to 30 cm. That
distance is from the front side of the microphone capsule to the
side of the clamped-in metal rod facing the microphone
7-
Press the button Start then the button Zero as shown in
Figure 2.5, then, Strike the right support (4) by using the
clamped rod (3) to start the timer which will stop when the
sound wave reaches the microphone. The reading may be
wrong (too long or too short) due to background noise.
Figure 2.4: The setting of the
Universal Counter
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8- Press on the hold button when the first reading is shown on the
screen.
Figure 2.5: The start, stop,
hold and zero buttons of the
Universal Counter
Very short and very high times are probable due to
srounding noise, soundwaves that travel through the
bench or the metal rods rebounding after being struck
which results in restarting the measurment after being
terminated. In all these cases you have to stop themeasurement and restart it again.
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9- Record the time shown on the timer screen when it stops.
10-Repeat steps 7 to 9 ten times to take more measurements for
the time. Record the results in the table.
11-Repeat steps 6 to 10 for three different distances 50, 70 and
90 cm. Record the results in the table.
12-Calculate the mean value for different measurements at each
distance.
13-Plot the relation between the distance on x-axis against mean
time on y-axis and calculate the slope, which is equal to the
reciprocal of the speed of sound.
14-
Calculate the speed of the sound (v= 1/slope.)
If the measurement
didnt terminate through
clear audiable sound try to
adjust the output voltage of
the microphone amplifier as
shown in Figure 2., until the
sound is detected by the
microphone, but avoid very
high voltages so that the
microphone cannot
discriminate background
noise.
Figure 2.6: Adjusting the
output voltage of the
microphone amplifier.
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2.5
Task2: Invistigationg Doppler effect
2.5.1
Setup
Figure 2.7 shows the setup used to measure the frequency shift
due to motion of detectpr relative to the sound source.
Figure 2.7: The apparatus used in studying the Doppler Effect of a
moving detector
1 Universal Counter 7Track, l=900 mm
2 Microphone with amplifier 8 Boss head
3 Support rod with hole, 100 mm 9 Sound head
4 light barrier 10Barrel base, PASS
5 Car, motor driven 11 Screen with plug6 Attachment for car
2.5.2 Procedure
1- Use the setup shown in Figure 2.7. Ensure that the sound head
and the microphone are adjusted at the same height and the
screen doesnt hinder the cars motion while passing the light
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barrier by adjusting the screen to be perpendicular to the
barrier. Cover the sound head with the cylindrical paper to
concentrate the beam toward the microphone.
2- Connect the microphone via the amplifier to the input of the
universal counter as shown in the Figure 2.7.
3- Connect the light barrier to gate 1 in the universal counter as
shown in the Figure 2.7.
4- Adjust the universal counter to measure the velocity of the car,
use the function velocity then set the Trigger to the case of
one pulse ( ), then press the SET button as often asnecessary for the LED alongside the Distance inscription to
light up. The display changes and the selected distance is
shown in the display with the unit "m". Select the distance
0.1m ( the width of the screen) by pressing the "+" or ""
button as shown in Figure 2.8. The counter is now ready to
measure the velocity of the car.
Figure 2.8: Adjusting the setting of the
counter to measure the cars velocity.5- Start the car motion and let the car move toward the fixed
microphone and determine its velocity by choosing carefully
its starting point so that it passes the light barrier at constant
velocity. Read the value of the detected velocity in the display
of the counter when the counting stops.
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6- Zero the counter
and restart it again
after restoring the
cars initial position
then repeat the last
step five times and
calculate the cars
average velocity
(v+). Record it in the
table.
7-
Adjust the universal
counter to measure
the frequency by
pressing the function Freq then choosing Analog mode as
shown in Figure 2.9.
8- Use the function generator to generate the sinusoidal sound
signal. Choose the signal type sinus then adjust the
frequency of the source sound to 5,000 Hz then adjust the
amplitude of the generated wave so that the counter displays
the correct value of the frequency (5,000Hz). A suitable value
of amplitude is about 1 volt.
9- Make sure the frequency in correctly measured on the screen
at the starting and ending points of the cars track.
10-Start the car motion with the same velocity in step (8), you
notice the detected frequency measured by the counter is
increased during the car motion.
11-
Press on the hold button when the car passes the light barrier.
Record this value in the table.
12-Repeat step 10 to 11 five times and calculate the average
frequency.
13-Use the start / stop button to begin / end the measurements
each time.
Figure 2.9: Adjusting the setting ofthe counter to measure the sources
frequency.
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14-Repeat steps 11-13 while retaining the cars velocity for the
frequencies (6,500 , 8000 & 10,000Hz).
15-Repeat the task with the car moves far away from the
microphone using the same frequencies. Record the results in
the table.
Due to the motor type, the cars forward and
backward velocities arent identical. Thus, the cars
velocity has to be measured again when changing the
cars direction of motion.