physical science 3 (sci 30105) chapter sound

Physical Science 3 (SCI 30105) Chapter 2: Sound ___________________________________________________________________________________________

Demonstration School of Suan Sunandha Rajabhat University © 2020 1

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1. Speed of sound waves 2. Reflection, Refraction, Interference, Diffraction of sound waves

- Reflection - Refraction - Interference - Diffraction

3. Power of a sound, Sound intensity, and Sound level - Power - Sound intensity - Sound level

4. Beats - Beat frequency - Average frequency

5. Resonance - String fixed at both ends - Pipe closed at one end and Pipe open at both ends

Closed at one end Open at both ends

6. Shock waves - vsource = 0

- vsource < vsound

- vsource = vsound

- vsource > vsound

7. Doppler effect

Chapter 2: Sound



Sound waves are generated by the vibration of an object.

Tuning fork Air particle Direction of travel of sound a.

b.

c.

d.

e.

Direction of travel of sound

Types of sound waves.

• Audible waves: frequency 20 – 20,000 Hertz

• Infrasonic waves: frequency < 20 Hertz

• Ultrasonic waves: frequency > 20,000 Hertz For example, bat sound

compression

compression

compression compression

compression compression rarefaction rarefaction

rarefaction

rarefaction

rarefaction rarefaction compression compression



1. SPEED OF SOUND WAVES .

The speed of sound in air depends on the temperature of the air:

vsound = 331 + 0.6T

where T = air temperature (oC)

Using this equation, one finds that at 25 oC, the speed of sound in air is approximately

vsound = 331 + 0.6 (25)

vsound ≈ 350 m/s

*** This equation works best at air temperatures -50 oC < T < 50 oC ***

Example 1.1: What is the wavelength of a sound wave in air at 20 oC if the frequency is 262 Hz.



2. REFLECTION, REFRACTION, INTERFERENCE, AND DIFFRACTION OF SOUND WAVES .

Reflection.

• The human ear can distinguish ‘echo’ from the original direct sound if the delay is more than 0.1 of a second.

• Sound waves are reflected only from objects larger than their wavelength. The advantage to bats of using high-pitched sound (ultrasonic) to echolate is that these sounds are carried on smaller waves and consequently permit the localization of smaller object.

Refraction.

• Lightning without thunder We hear thunder when the lightning is close to us, but we often do not hear the thunder

for distant lightning because of refraction – Sound waves propagating through air are bent and undergo refraction when the air temperature varies. The air near the ground is warmer than the upper air, so the speed of sound near the ground is greater. The sound will be refracted and bent away from the ground.

Interference.

• Two identical loudspeakers emit sound waves toward each other. When they overlap, identical waves traveling in opposite directions will combine to form standing waves.

Diffraction.

• Sound waves bend around the corner of building.



3. POWER OF A SOUND, SOUND INTERNSITY, AND SOUND LEVEL .

Power of a sound (P).

Power of a sound is defined as the rate at which the energy transported by the wave or the energy that the sound source emits per unit time. The unit of power is Joule per second (J/s) or Watt (W).

Sound intensity (I).

Sound intensity is defined as the power of a sound per unit area.

I ≡ P

A

The unit of sound intensity is Watt per square meter (W/m2).

For a point sound source, the sound will radiate in all directions equally as a spherical surface (A = 4πr2) with the sound source at the center of the sphere. Hence, the intensity of a sound wave at a distance r from the source is

I = P

4πr22

The intensity decreases with increasing distance r from the source according to the inverse-square

law.

Note: Threshold of hearing I0 = 1.0 × 10–12 w/m2



Example 3.1: A point source emits sound waves with an average power output of 80.0 W. a) Find the intensity 3.00 m from the source.

b) Find the distance at which the intensity of the sound is 1.00 × 10-8 W/m2. Example 3.2: A siren on a tall pole radiates sound waves uniformly in all directions. At a distance of 15.0

m from the siren, the sound intensity is 0.250 W/m2. At what distance is the intensity 0.010 W/m2.



Sound level (β).

Sound level is defined as the logarithm measure of sound intensity.

β = 10 logI

I0

The unit of sound level is decibel (dB)

Sound intensity (I) Sound level (β)

10-12 d

10-11 d

10-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

1



Example 3.3: Find the sound level of the sound wave with sound intensity 3.2 × 10-7 W/m2

Example 3.4: What sound intensities correspond to 48 dB?

Audible waves: f = 20 – 20,000 Hz I = 10–12 – 1 w/m2 β = 0 – 120 dB



• The different between any two sound levels is related to the corresponding intensity by

β1 - β

2 = 10 log (

I1

I2

)

β1 - β

2 = 10 log (

P1

4πr12

P2

4πr22

)

If the power of a sound does not change P1 = P2, then

β1 - β

2 = 10 log (

r2

r1

)2

β1 - β

2 = 20 log (

r2

r1

)

Example 3.5: Consider an idealized bird (treated as a point source) that emits constant sound power,

with intensity obeying the inverse-square law. If you move twice the distance from the bird, by how many decibels does the sound intensity level drop?



Example 3.6: Two identical machines are positioned the same distance from a worker. The intensity of

sound delivered by each operating machine at the worker’s location is 2.0 × 10-7 W/m2. a) Find the sound level heard by the worker when one machine is operating. b) Find the sound level heard by the worker when two machines are operating.

Loudness is a psychological response to a sound. It depends on both the intensity and the frequency of the sound. As a rule of thumb, a doubling in loudness is approximately associated with an increase in sound level of 10 dB. If the loudness of the machines in this example is to be doubled, how many machines at the same distance from the worker must be running?



• An audiogram of the human hearing The audiogram shows the values of the sound level threshold as a function of frequency. It

shows how sound levels need to be at different frequencies for you to hear them.

According to the diagram, the sound level threshold is dependent on frequency.



Pitch.

• Low pitch (low frequency) → Bass

• High pitch (high frequency) → Treble

Quality of sound.

The quality of the sound is part of what allows you to identify instruments playing the same note. For example, you can differentiate between a guitar, piano, or a flute playing the same note.

Musical sounds have wave functions that are more complicated than a simple sine function. The pattern is so complex because the musical instruments generates many frequency at the same time. These frequencies are called ‘harmonics’. The lowest frequency is called the ‘fundamental frequency’ or ‘first harmonic’. The frequencies of the remaining harmonics are integer multiples of the fundamental frequency.

The wave patterns produced by a musical instrument are the result of the superposition of harnonics. Two tones produced by different instruments might have the same fundamental frequency but sound different because of different harmonic content.

Fundamental frequency or first harmonic

second harmonic

third harmonic

resultant wave

time

time

time

time



4. BEATS .

Beating is the periodic variation in amplitude at a given point due to the superposition of two waves having slightly different frequencies. A listener would hear a sound of periodically varying loudness.

Beat frequency (fB).

Beat frequency is the number of amplitude maxima one hears per second. It equals the difference in frequency between the two sources

fb = |f1 - f2|

Note: At frequency differences greater than about 7 Hz, we no longer hear individual beats. Average frequency.

The resultant wave has a frequency equal to the average frequency:

f average = f1 + f2

2

For instance, if one tuning fork vibrates at 438 Hz and a second one vibrates at 442 Hz, a listener

would hear a 440-Hz sound wave go through an intensity maximum four times every second.

Dis

pla

cem

ent

time (s)

0 1 2 3 4



5. RESONANCE .

The frequency at which a system tends to oscillate in the absence of any driving or damping force is called ‘natural frequency’.

Resonance is the peaking of the amplitude when the frequency of the driving force is near the natural frequency of oscillation. For example, building up the oscillations of a child on a swing by pushing with a frequency equal to the swing’s natural frequency.

• Fundamental frequency: lowest frequency

• Harmonic: All integer multiples of the fundamental frequency

• Overtone: Any frequency greater than the fundamental frequency

String fixed at both ends.

fundamental frequency

second harmonic

third harmonic



Pipe closed at one end and Pipe open at both ends.

Resonance occurs when the air in the pipe is stimulated by sound waves that have the same frequency as the natural frequency of the air in the pipe.

• A ‘tuning fork’ is vibrated near the top of the pipe. There are many forks frequencies that can cause the resonance of the air in one pipe.

Pipe closed at one end Pipe open at both ends

fundamental f fundamental f first harmonic first harmonic

first overtone first overtone third harmonic second harmonic

second overtone second overtone fifth harmonic third harmonic

• A tuning fork vibrating at an unknown frequency is placed near the top of the pipe. The length of the air column can be adjusted. The experiment shows that there are many positions of water levels in the pipes that cause resonance.

B

E

A

D

C

F

Displacement

Position

Displacement

Position

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Example 5.3: A simple apparatus for demonstrating resonance in an air column is depicted in figure below. A vertical pipe open at both ends is partially submerged in water, and a tuning fork vibrating at an unknown frequency is placed near the top of the pipe. The length L of the air column can be adjusted by moving the pipe vertically. The sound waves generated by the fork are reinforced when L corresponds to one of the resonance frequencies of the pipe. For a certain pipe, the smallest value of L for which a peak occurs in the sound intensity is 9.00 cm.

a) What is the frequency of the tuning fork? b) What are the values of L for the next two resonance conditions?



6. SHOCK WAVES .

Shock waves occur when the speed of source exceeds the wave speed.

vsource = 0.

vsource < vsound.

• If the source is moving toward the listener, the frequency heard by the listener is __________.

• If the source is moving away from the listener, the frequency heard by the listener is __________. vsource = vsound.

v source > v sound.



7. DOPPLER EFFECT .

Doppler effect is a phenomenon that occurs when a source of sound and a listener are in motion relative to each other causes the frequency of the sound heard by the listener is not the same as the source frequency.

where u = velocity of sound wave

vs = velocity of source vL = velocity of listener f0 = frequency of sound wave emitted from the source

fL = frequency heard by the listener

vs

vs

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vL

vs

vL

vs

vL

vL

vL vs

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physical science 3 (sci 30105) chapter sound

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