PHYSICS of SOUND Grade11

Feb 2008 C.M. Bali 1

PHYSICS of SOUND Grade11

With CRO and Signal Generator

C.M. Bali, BSc (Hons) MSc MEd TeacherDept of Mathematics and Science (Physics)Miles Macdonell Collegiate, Winnipeg


Grade 11Physics Outcomes for Sound

• S3P-1-17: How sounds are produced, transmitted and detected • S3P-1-18: Analyze an environmental issue concerning sound• S3P-1-19: Design, construct, test, and demonstrate technological devices to

produce, transmit, and or control sound waves for useful purposes• S3P-1-20:Intereference of sound waves. • for resonance• S3P-1-22: Speed of sound in air• S3P-1-23: Effect of temperature and other factors (including materials) on the

speed of sound. • S3P-1-24: Doppler Effect (Qualitative treatment) • S3P-1-25: Decibel scale (Qualitative, example of sound)• S3P-1-26: Applications of sound waves (hearing aid (for Mr. Bali), ultrasound,

stethoscope, cochlear implants (also perhaps for Mr. Bali))• S3P-1-28:Examine the octave in a diatonic scale in terms of frequency

relationships and major triads.


Cathode-ray Oscilloscope (CRO)or oscilloscope for short


Sound of Music(You can even play the game ‘Guess that Tune’)

Some musical instruments and their characteristic sound

Click on the link below

Choose the instrument

Click play

• http://www.dsokids.com/2001/instrumentchart.htm

• As you play a tune, you should display the sound pattern on the CRO.

S3P1-17

http://www.dsokids.com/2001/instrumentchart.htm


Experiments with CROand signal generator

1. Frequency of a tuning fork (Slide 9)2. Experiment to explore frequency, amplitude, pitch, intensity and

loudness of Sound (Slide15)3. Comparing loudness at different distances (Slide 18)4. Beat Frequency (Slide 21)5. Speed of sound using progressive waves (Slide 30)6. Speed of sound using stationary waves (Slides 42 and 43)7. Standing waves on strings. Speed of waves on strings (Slide 45)8. Quality (timbre) (Slide 47)9. How to show the velocity of a wave depends on tension and mass

per unit length of string. (Slide 49)10. Resonance (Slides 59)11. Resonance (Slide 62)12. Demonstration of phase and measurement of speed of sound (68)13. Variation of intensity of sound with distance (Question) (Slide 70)


The function of oscilloscope

The basic function of an oscilloscope is to plot a graph of

Voltage versus time


Voltage versus time

Voltage (Y)

1cm*5ms/cm =0.005 s

2cm*2v/cm = 2 volts

2cm*5ms/cm=10 ms =0.010 s = period

Time (X)

Y AMPLIFIER: 2V/cm TIMEBASE, t : 5ms/cm

Timebase

Ch 1Y amplifier


SOUND:The maximum range of human hearing

includes sound of

Frequencies15-18,000 Hz

(Microsoft Encarta Encyclopedia. CD-ROM. 2000)


Measurement of frequency of a tuning fork

Microphone PreamplifierStorage / Analogue

switch

Time base

To CH 1

S3P1-17S3p1-19

See next slide for details

Save All switch


Measurement of the frequency of a tuning fork

1. Connect the apparatus as in the previous slide. All switches should be in the up position.

2. Turn oscilloscope on. Adjust the intensity and focus control.3. Timebase should be calibrated (Turn ‘Var Sweep’ clockwise).4. Strike the tuning fork and hold the prongs close to the mike.5. Turn the time base switch until a good, well spaced, fairly stable

sine signal is obtained. 6. Press Storage / analogue switch in. Freeze the trace by pressing

in the Save All button.

7. Measure peak to peak horizontal distance and multiply it by time base scale.

8. Frequency = 1 / period (Hz)

9. Before repeating, press out Storage/analogue.


Tuning Fork Observations

T Fork Timebase Pk to Pk (x)

Period/sec Frequency/Hz

C126 2 ms/cm 3.9cm 7.8ms = 0.0078s 1/0.0078=128 Hz

D288 1 ms/cm 3.5cm 3.5 ms = 0.0035s 1/0.0035 =285 Hz

E320 1ms/cm 3.1cm 3.1 ms=0.0031s 1/0.0031= 322 Hz


% Error% uncertainty

(I

% Error *100

For Fork C126 :

(128 126)% *100 1.6%

126

uncertainty in measured value% Uncertainty = *100

Measured ValueFor Fork C126 :

0.1cm%Uncertainty = *100 2.5%

3.9cm

Measured value Accpted valueAccpted value

ErrorHz

am assuming oscillscope controls are 100% accurate)


Sound: Longitudinal Mechanical Waves

• Sound is a longitudinal wave, but they are drawn as transverse waves, to make the information clear. Sound is a mechanical wave as it requires a material medium such as air or metal or any other material for its transmission as well as a source of energy that disturbs the material medium.

• Click on the link below to see longitudinal and transverse waves. Pay attention to the source of disturbance and the material medium that transmits the disturbance..

• Focus on any one particle (a black dot) of gas to see its to and fro movement in the direction of the flow of the wave’s energy: in this picture sound wave progresses horizontally to the right.

• http://www.kettering.edu/~drussell/Demos/waves/wavemotion.html

http://www.kettering.edu/~drussell/Demos/waves/wavemotion.html


Sound Characteristics

Frequency

Amplitude

Pitch

Intensity

Loudness

Quality or Timbre


Experiment to explorefrequency, amplitude, pitch, intensity and loudness of

Sound

Microphone Preamplifier

Time base

To CH 1Speaker

Signal Generator

Constant distance

Frequency dial

Amplitude dial

Frequency display


D

S3P-1-19,1-27


Frequency and Pitch

• Set up the experiment as in the previous slide (15).

• Turn on the oscilloscope and the signal generator.

• Investigate the pitch by listening to the sound from the speaker as the frequency is increased and then decreased. Keep amplitude (peak to peak distance on the oscilloscope) and D constant.

• Students should see that the higher the frequency the higher the pitch.

• (You can do this by using tuning forks of various frequencies, but it is difficult to keep the amplitudes constant)

S3P-1-27


Intensity and loudness of Sound

• See slide # 10 for experimental set up.• Intensity = power per m2 (W m – 2)

• Power is proportional to the square of the amplitude of the wave. (Follows from SHM)

• Amplitude of the CRO trace is proportional to the amplitude of the sound wave hitting the microphone.

• Thus intensity of sound is proportional (not equal) to the square of the amplitude of the CRO trace. [CRO measures voltage]

• Loudness:

(in be

C

D

D C

D D10 10

C C

Suppose sound C has intensity = I

and sound D has intensity = I

If I >I , then D is louder than C.

Loudness of D relative to C is given by :

I IdB = 10* log ( decibells) ; B =log

I I)lls

A

2D D

10 102CC

Since intensity is proportinal to the square of the CRO trace amplitude,

A AdB = 10* log =20* log where A is amplitude

A

S3P-1-27


Comparing loudness at different distances

• Set up the experiment as shown below (also see slide 10).• Place microphone 50 cm from the speaker and adjust the volume on the signal

generator to get a CRO trace of 1 cm amplitude.• Move the microphone by 20 cm at a time towards and away from the speaker.

Find the dB level of the sound relative to the reference point.

MicrophoneSpeaker

50 cm 100cm0 cm

Signal generator

Distance = 50 cm A (50) = 1. 0 cm Relative Loudness = 0

dist = 30 A (30) = dB = 20 * log {A(50) / A(30)} =

dist = 10 cm A(10) =

dist = 70 A(70)- =

dist = 90 cm A(90) =

S3P-1-27


Double Beam OscilloscopeIt has two inputs CH1 CH2 and a common timebase

Therefore, you can display and compare

two signals (graphs) simultaneously.


Beat Phenomenon

When two sound waves

of different frequencies

interfere

we hear sound

whose amplitude

varies

periodically.


How to show beat phenomenon and measure beat frequency

Signal Gen 1

Signal Gen 2

To Red and Black terminals

To red and black terminals

To CH1To Ch 2

Speaker 1 Speaker 2

499Hz

510Hz

Timebase

Measure Beat period

Beat periodStore All switch

Storage / analogue switch

Bt freq = 1 / Bt period Ch1, Ch2, Dual, Add SWITCHCh1,Ch2, Dual, Add SWITCH

OutcomesSP3-1-17Sp3-1-19S3P-1-20

See slide 26 for details


Measurement of beat frequency

When two sinusoidal functions of different frequencies are added

we get:

Time

Displacement

TbBeatB

1f =

T


Beat Frequency FormulaIf two sinusoidal disturbances, y1 and y2, of frequencies, f1 and f2, are added,

the principle of superposition gives:

1 1 1 1

2 2 2 2

1 2 1 2

1 2 1 2

1 2

sin where 2

sin where 2

sin sin

2sin *sin2 2

2sin represents2

the slow varying amplitude of

α - β α+ βsin

2 2

y t f

y t f

Y y y t t

Y t t

Using : sinα+sinβ = 2sin

t

1 2

the enveloping curve (amplitude modulation) in the previous slide.

The envelope amplitude is zero when = n2

Therefore, sound has zero amplitude with an angular period of .

Therefore, time

t

beat1 2

1 2 1 2

,period, T for zero sound is given by 2

2 2,

21 1 2,

2 2 2

beat

beat

beatbeat

T

Therfore T

fTherefore f fT

Not for grade 11students but suitable for grade 12


Beat Frequency Formula: A simple approach using relative speed

• Imagine two athletes, A and B, running to and fro on a straight track, a total distance of 2L.• Suppose A takes x seconds and B takes y seconds to complete one to and fro distance on the track .• Therefore, x and y are the periods of A and B• Frequency of A =1/x, and of B= 1/y• Let us assume they will be running for some time!• We want to know how often they meet or cross each other. To be more precise, how many times per

second they will cross each other; that is, what is their beat frequency?

m

m

2LSpeed of A = /sec.

x2L

Speed of B = /sec.y

Consider B to be at rest, at the start line, and A running relative to B.

2L 2L y - xSpeed of A relative to B = - =2L

x y xy

Time for A to go round once, and meet

BA

B again2L xy

=Beat period = =y - xy - x2L

xy

1 1 y - x y xFrequency with which this occurs = = = = -

xyBeat Period xy xy xyy - x

1 1⇒ - = f - f

x y

Students should be able to do this proof

SP3-1-20


Beat Frequency Formula: A simple approach using relative angular speed (in degrees)

• Imagine two athletes, A and B, running around a circular track.• Suppose A takes x seconds and B takes y seconds to go round the track once.• Therefore, x and y are the periods of A and B• Frequency of A =1/x, and of B= 1/y• Let us assume they will be running for some time!• We want to know how often they cross each other. To be more precise, how many times per second they will cross

each other; that is, what is their beat frequency?• You can go through this argument using radians, and will get the same result.

0

0

0 0

degrees

degrees

360The Angular speed of A = /sec.x

360The angular speed of B = /sec.

yConsider B to be at rest, at the start line, and A runs relative to B.

360 360The angular speed of A relative to B = -

x y

A B

y - x=360

xy

Time for A to go roumd once, and meet B again360 xy=Beat period = =

y - xy - x360xy

1 1 y - x y xFrequency with which this occurs = = = = -

xyBeat Period xy xy xyy - x

1 1⇒ - = f - f

x y

Students should be able to do this proof


Measurement of Beat frequencyExperimental Procedure

1. Set up the experiment as in slide 21.

2. Set Signal 1 to 490 Hz, and Signal 2 to 509 Hz. You should hear beating sound.

3. Set Oscilloscope to: Dual, time base to 20ms/Div, Storage/ analogue switch in, and Y1 and Y2 to an appropriate scale. You should see two traces somewhat out of phase.

4. Now press the Add switch.

5. With the storage / analogue switch in, Press Store All switch.

6. This should freeze the trace.

7. Measure Beat period.

8. Calculate Beat frequency.


Beat Frequency Observations

Speaker 1

Freq / Hz

Speaker 2

Freq / Hz

Time base Beat period

Beat period /seconds

Beat frequency/ Hz

510 514 50 ms/ cm

5.6 cm 0.050*5.6=0.280 s

1/0.280=

3.57= 4Hz

201This was a good graph

210 20 ms/cm

5.4cm 0.108 s 9.25 Hz

1010This was a good graph

900.5 2 ms/ Div

4.5cm 0.090 s 11 Hz


Sound as Progressive wave

A simple argument for students

• Progressive waves carry energy from one point to another.• As the wave particle oscillates once, the wave moves forward by

one wavelength.• If the particles oscillates f times per second, the wave will move

forward f wavelengths.• Thus:

*f

*f


Speed = frequency * wavelengthA more rigorous derivation

y= a sin(ωt - kx) where y = displacement of wave, a= amplitude(ωt - kx) is called the phase of the wave.ω= 2πf

2πk =λ

Suppose in time Δt, the wave progresses by a a horizontal distance of Δx.This means that the of the wave is the same at t and at t+ Δt.This means the is the same at these two times.Thus, (ωt - kx)= (ω(t+ Δt)- k(x+ Δx)

(ωt - kx)=(ωt+kx+ωΔt - kΔx) ωΔt - kΔx= 0 kΔx

disp

= ωΔt

lacement

velocity

ase

=

ph

Δx ω 2πf= = =2πΔt k

v

λ

= fλ

Not for students


Measurement of speed of soundusing progressive waves

A B C

E

F

0cm100 cm

A = Signal generatorB = SpeakerC = Mini MicrophoneD = Block of wood for supportE = PreamplifierF = Mitre rule

D

Note this reading when both

signals are in Phase

Move D until both signals are in phase again.

Note this point

This distance, d = One wavelength

Timebase

Frequency can be readDirectly from Signal generatorOr from the oscilloscope trace

To Ch1 input To Ch2

Double beam

S3P-1-17, 1-19,1-22

See slide 32 for details

Dual mode


Measurement of speed of soundUsing progressive waves

1. Set up the experiment as shown on the previous slide

2. We know from basic experiments that speed of sound is about 340 m / s.

3. We want to measure a wavelength of say 20 cm. This informs us that the frequency should be around 340 / 0.20 = 1700 Hz.

4. We will use the frequency of sound at 1.5 KHz to 3.0 kHz.

Sig. Gen freq Freq from CRO Wavelength Speed using CRO freq

% uncertainty

1470 Hz (34.0 -10.0) =2 4. 0 cm 0.24*1470 = 3 50 m / s About 5%

1960 Hz (36-0)/2 = 18cm 0.18*1960 = 352 m / s See next two slides

2439 Hz 29.0-14.5 = 14.5 cm 0.145 * 2439 = 353 m / s

2940 Hz 23-11.4 = 11.6 cm 340 m/sec


Errors and uncertainties

Students can calculate

errors and uncertainties in the beat frequencies

from data in previous slide


How to calculate uncertainties

v =fλ1 1 1f = = , ∴v = d

Period τx τxx = horizontal peak to peak distance on CRO screenτ= time base setting d = distance( peak to peak) moved by microphone=wavelength

δv δx δd∴ = +v x d


Calculating Uncertainties• Sig. Gen freq Frequency from CRO Wavelength Speed using CRO freq• 1500 Hz 1470 Hz (34.0 -10.0) =2 4. 0 cm 0.24*1470 = 3 50 m / s

δv δx δd= +

v x dx = 3.4 ± 0.1cm (CRO Pk - Pk)

d = 24.0 ± 0.5cm (Microphone Pk - Pk)

δv 0.1 0.5= + = 0.05 = ±5%

v 3.4 24.0


Theory of UncertaintiesErrors always add, hence absolute signs.

a b

c

a-1 b b-1 a a b

c c c+1

where x, y and z are indepenedent variables,

and f is the dependent variable, i.e. it is a function of x, y and z.

x yLet f =z

f f dfδf = δx + δy + δzx y z

ax y by x -cx yδf = + +z z z

δf δyδx δz= a +b± +cx yf

∂ ∂⇒∂ ∂ ∂

⇒

⇒ z

Thus, fractional uncertainty in f = fractional uncertainty in x* exponent value of x +...

δx is called the fractional uncertainty in x.

x

Not for students


x ±yUncertainty in f =

p ±q

( )

( )

m mx+ y = x+ y; And e

x ym rrors always add

Let m x y

n p q

m x y

Similarly n p q

mf

nf m n

f m n

m nf f

m n


Uncertainties

A measurement can never be perfect.

The minimum error in a measurement is equal to the instrumental error.

If the variation in the measurement is much bigger than the instrumental error, then ignore the instrumental error, but use the deviation or standard deviation from the mean as a measure of uncertainty in the mean.


Example

1/ 2

1/ 2

1 12 2

12

Tv

Tv

v Tv T

Tv v

T


Conditions for setting up

Stationary Waves

When two progressive wavesof the same frequency and wavelength

And traveling in opposite directions And

interfere then, at certain wavelengths,

that satisfy the boundary conditions,

Stationary waves are formed.


Mathematics of Stationary Waves

1

2

1 2( where Y =displacement of resultant wave)

y =asin( ωt-kx): Wave moving to the right.

y =asin( ωt+kx): Wave moving to the left.LetY =y +yY =asinωtcoskx-acosωtsinkx+asinωtcoskx+acosωtsinkxY =2asinωt.coskxY =[2acoskx] sinωt

This equation shows that the maximum amplitude is 2a.And , net dispalcement, Y, is a function of distance, x. When x is such that cos kx is zero, t

( Where 2a coskx represents amplitude of Y)

hen the amplitude is zero, i.e. .When x is such that cos kx is 1, then amplitude is maximum( 2a) ,

it is a node pointit is an antinode p i.e. oint.

Not for grade 11 students


Standing wavesFrom the University of Toronto

http://www.upscale.utoronto.ca/GeneralInterest/Harrison/Flash/#sound_waves

• http://faraday.physics.utoronto.ca/IYearLab/Intros/StandingWaves/Flash/reflect.html

• http://faraday.physics.utoronto.ca/IYearLab/Intros/StandingWaves/Flash/standwave.html

• http://faraday.physics.utoronto.ca/IYearLab/Intros/StandingWaves/Flash/sta2fix.html

• http://faraday.physics.utoronto.ca/IYearLab/Intros/StandingWaves/Flash/sta1fix.html



http://faraday.physics.utoronto.ca/IYearLab/Intros/StandingWaves/Flash/reflect.html

http://faraday.physics.utoronto.ca/IYearLab/Intros/StandingWaves/Flash/standwave.html

http://faraday.physics.utoronto.ca/IYearLab/Intros/StandingWaves/Flash/sta2fix.html

http://faraday.physics.utoronto.ca/IYearLab/Intros/StandingWaves/Flash/sta1fix.html


Speed of soundusing stationary waves

Speaker

Signal Generator Amplitude dial


S3P-1-19,1-27

Shiny reflector

MicrophoneDual Mode

Speaker signal

Microphone signal (White dotted line): almost flat showing a node position at microphone

CH 1

CH 2


Speed of sound using Stationary Waves

1. Set up the experiment as in the previous slide (slide 42)2. Move the screen until the microphone signal is very small (see slide 45 for analogy).

3. Now keep the screen still, and move the microphone gently.

4. Measure the distance between two nodal points: this is equal to the distance moved by the microphone between two successive points where the CRO signal is very small, while the reflector is kept at the same position. This distance is equal to half the wavelength. Thus, the wavelength is twice this distance.

5. Find speed of sound by multiplying the wavelength by the frequency, which can be seen on the signal generator.

6. Find uncertainty in the speed.

7. Find error in the speed.

Distance Wavelength Frequency Speed uncertainty Error


Natural Frequencies and Resonance

All objects have certain natural frequencies of oscillations. For example, a swing can oscillate back and forth at a certain frequency that depends on its dimensions. If you push this swing gently but periodically, such that the frequency of your push is exactly the same as the natural frequency of the swing, then energy can flow from the your body into the swing. The energy in the swing can build up to the extent that the swing may become very unstable (very high amplitude of vibration) and even break !! Three dimensional objects have many natural frequencies of vibrations.

Show: Tacoma Narrows Bridge Falls

http://www.boreme.com/boreme/funny-2007/tacoma-bridge-p1.php

The phenomenon in which energy can pass easily from one object (A) into an other (B) if it is fed at the natural frequency of the other (B)

object is called resonance.

SEE NEXT SLIDE:




How to set up a stationary (resonating) wave on a string

B

AD

E

A: Signal GeneratorB: VibratorC; StringD PulleyE: Weight to provide tension in string

Table

C

1st Harmonic

2nd Harmonic

3rd Harmonic

4th Harmonic

1:

2

2

n L for nth harmonic

L

n

Vibrates with small amplitude

Large amplitude of vibration

S3P-1-21

AN ANN N N

AN


Harmonics and Overtones• See Previous Slide 45 for experimental set up.

1. Look at the frequency on the signal generator as you set up stationary waves on the string.

2. The frequency is lowest when first harmonic is set up. This frequency is called the fundamental frequency.

3. As the number of harmonics increases, frequency increases. (note: the nth harmonic has n half waves.)

4. OVERTONES: When an instrument (e.g. a taut wire as in the experiment) is plucked, it produces a sound which is a combination of many harmonics.

5. Overtones can be displayed on the CRO and analyzed and

shown to be composed of harmonics of that taut wire.

6. The first overtone is the first harmonic, the second overtone is the second harmonics, and so on.

S3P-1-27


Quality or Timbre of Sound

• When an instrument is played it does not produce a note of just one frequency. It consists of the fundamental frequency and higher harmonics with different amplitudes. The resultant wave is the superposed sum of various harmonics. Thus the resultant wave is different from that of the fundamental frequency. The ear responds to the fundamental frequency, but it also senses the presence of higher harmonics. This sensation due to the presence of many harmonics is called the quality of sound. Thus different instruments, and even the same instrument, generate sounds of different quality, even though they may be playing the same fundamental frequency.

Play a tune from slide 4

http://www.dsokids.com/2001/instrumentchart.htm and observe the trace on the CRO

http://www.dsokids.com/2001/instrumentchart.htm


Analysis of Quality or Timbre of SoundWith a graphing calculator

Use TI83 or the link below for a graphing calculator:

• Without Fourier analyzing, we can see that a periodic non-sinusoidal function is the sum

of many sinusoidal functions. Graphing Calculator:

http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html

• Set window to : x min (-5), x max (5), y min (-2), y max (2); Xscl and Yscl =0.1• Mode Radians.

• Example: draw a graph of: Y = 1sin (x) + 0.75 sin (2x) + 0 sin (3x) +0.20 sin (4x): You should see that Y is periodic but non-sinusoidal, the period being different from the periods of the component harmonics,(also draw individual graphs)

• Thus quality is due the presence of many harmonics.

http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html


Experiment The speed of a wave on a string

• Set up the experiment as in slide 45. Record resonant frequency for the first, second and third harmonic. Enter the observations in the table below. Find average speed.

Different students can try same material of different thicknesses and tensions.

Precautions: Keep tension constant. Check L has not changed.

Length of string,

L / m

N = Number of loops, or harmonics

wavelength =

2L/(N) / m

Freq, f / Hz (from Sig. Gen)

v = freq * wavelength

(m / s)

1

2

3

4


An Experiment for IB or AP Students

Problem: • The speed of a wave on a string is thought to depend on the tension

in the string. Investigate the relationship between speed and tension.

Idea:

Let us suppose that the speed depends on the tension.

We don’t know how it depends.

[Theory must always precede experiment, even if we don’t realize it.]

: ;T

v T tension in string mass per unit length of string

nv kTSo assume – requires some thought!


Theory and Analysis of data

n

1/2

ln(v) vs. ln(T

v = kT : k is a constant.Take logs to base e :

ln(v)= ln(k)+n ln(T)Therefore a graph of should be a straight line, with slope = n.

1If n is , then the relationship is T = kT

2

)

= k T


Experimental details

• Set up the experiment as shown in slide 45.• Conduct the experiment in second harmonic.• Keep the length of the string constant.• Apply different weights to vary the tension.• For each weight, note f on signal generator. The wavelength is L.• Therefore the speed of the wave is f * L.

• Record the observations in the table below:


DataMass / kg

Weight (mg) / N

Wavelength / m

Frequency / Hz

Speed

m /s

1.300

1.400

1.500

1.400

1.500


Graph of ln(V) vs. ln(T)

ln (T)

ln (v)Gradient = 0.5

O

ln (K)


• Discussion

• Conclusion

At a more simple level,

students can plot Velocity versus Sqrt of T.

A straight line of slope 1will uphold the relationship between velocity and tension.


Velocity and mass per unit length

: We need to discover the value of n.

If n turns out to be be , then v can be said to be equal to .

Take logs to base e:

ln ln ln

Therefore a graph of vs. should be a straight linlnv

1 k-

2

ln e o

nv k

v k n

slope n

y intercept

f

and = ln k. ln v

ln

Slope should be – 1/2


Experimental details

• Set up the experiment as in slide 45.• You should use wires of the same material but different thicknesses. • Use the same length of wire, keep tension the same. Do experiment in 2nd harmonic

to keep calculations easy – this makes wavelength = L• Plot ln . lnv vs

L / m Mass/m Tension

Constant

f / Hz2nd Harmonic

V = f * L ln V ln (mass /m)


Analysis

• Graph

• Calculations of slope etc

• Discussion

• Conclusion.


ResonanceMeasurement of speed of sound using a resonance tube

Demonstration of nodes and antinodes with sound

RB

FA

Speaker

OscilloscopePreamp

Mike

Tube

Signal generator

Freq dial

Amplitude dial

L = wavelength / 4

Metre ruleTo Ch 1 or 2

Shows Large signalAt Resonance

To show node at the bottom gently lower the microphone to the bottom of the cylinder

SP3-1-20, 1-21, 1-22


Data

1

44.5

( ) 186

144.5

444.5*4 178 1.78

( ) 331

L cm

f R Hz

cm m

v f R ms


Discussion of results:Note: Accepted value=332+0.6T/degC

• So at room temp, v =332+.6*20=344 m / s• End Correction: depends on the tube diameter• Measurement techniques, including parallax

Include % error

Conclusion:


ResonanceMeasurement of speed of sound using a resonance tube

Demonstration of nodes and antinodes with sound

RB

FA

Speaker

OscilloscopePreamp

Mike

Tube

Signal generator

Freq dial

Amplitude dial

Metre ruleTo Ch 1 or 2

Shows Large signalAt Resonance

2L n

n = number of loops or harmonics, here n = 1

Tube open at both endsSP3-1-20, 1-21, 1-22


Resonance Tube (both ends open) Observations

First resonant frequency =359 Hz

Length of tube = 45.5 cm1

45.52

91 0.91

359

327 /

2 0.52%

359 45.5

L cm

cm m

f Hz

v f m s

v fv f

LL

v f Lv f L


Phase relationships and oscilloscope

Consider two functions (or voltage signals) y (t) and x (t) where:

( ) sin( )

( ) sin( ) sin cos cos sin

x t a t

y t a t a t a t

phase difference


The principle of superposition gives:

Case 1: Phase Difference0

sin sin

2 sin

R x y a t a t

a t

,

( sin )

Alsoy xboth t

(1)

(2)

R=Resultant displacement as a function of time

A relation independent of time, or true at all times Y-axis

X-axis


Case 2 : Phase Difference0 )( 180or

( ) sin( )


x t a t

y t a t a t a t

cos180 = -1, and sin180 = 0

Therefore, ( ) sin( ) siny t a t a t

( sin ) ( sin ) 0x y a t a t

( )Andy x at all times Lissajous

relationX-axis /cm

Y-axis

Timebase off, X-Y in

Time

Y cm


Case 3 : Phase Difference0 )

2( 90or

( ) sin( )


x t a t

y t a t a t a t

cos 90 = 0, and sin 90 = 1

Therefore, ( ) sin( ) cosy t a t a t ( sin ) ( cos ) (sin cos )x y a t a t a t t

2 2 2 2 2 2 2

2 2 2

cos

:

sin( )x y t a t a

y a circle of radius a

Anda

at all timesx

Lissajous relation X-axis /cm

Y-axis

Timebase off, X-Y in


How to demonstrate change in phaseSpeed of sound using this method.

A B C

E

F0cm

A = Signal generatorB = SpeakerC = MicrophoneD = Block of wood for supportE = PreamplifierF = Mitre rule

D

Timebase

To Ch1 input To Ch2

Double beam

Move the microphone , with the X-Y switch pushed inThe trace should change: you should see straight line (+ & - slope) and circleWavelength = distance moved by the microphone for the phase to change by 2pi radians.

X-Y switch Pressed IN


0 X-axis

Y-axis

With time base off,And X -Y switch in

Sine function with double amplitude

X-Y switch out, timebase on Lissajous Figure

Add Switch on

Sine function with Zero amplitude

2


QuestionHow would you investigate the variation of sound intensity

with distance?

Signal Gen

Spe

aker

1

Timebase

Store All switch

Storage / analogue switch

Ch1

Pre AmplifierMicrophoneDistance = x


Doppler Effect

Use internet sources to demonstrate this effect

sound observerobserved '

sound source of sound( car)'

original fromsource of sound( car)

v ±vf = :

λuse positive if observer approaching the source of sound,

negative if receeding

v ±vλ =

f

Use negative if source of sound moving towards the observer,

use positive if moving away from the observer.

S3P-1-24


End

C.M. Bali, BSc (Hons) MSc MEd CPhys MInstPTeacher

Dept of Mathematics and Science (Physics)Miles Macdonell Collegiate,

Winnipeg, Canada

PHYSICS of SOUND Grade11

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