experiment 2 manual - speed of sound.pdf

8/10/2019 Experiment 2 manual - Speed of sound.pdf

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Waves LAB 2

14 MEASURING THE SPEED OF SOUND IN AIR - DETECTINGDOPPLER EFFECT

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.

experiment 2 manual - speed of sound.pdf

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