ea notes (scen 101), tillery chapter 5 wave motions … notes (scen 101), tillery chapter 5 wave...

EA Lec Notes (Scen 101) Til 7 Ed-Chap5 - 1 - Printed - 10/31/2007 9:36 PM

EA Notes (Scen 101), Tillery

Chapter 5

Wave Motions and Sound

Introduction

• Microscopic molecular vibrations determine temperature (last Chapt.).

• Macroscopic vibrations of objects set up what we call Sound waves.

• Waves move through space and carry energy away from the source.

• Several concepts depend on wave motion. (Wave Types)

• In THIS chapter: Mechanical Waves: Elastic Materials & Sound. These waves carry Kinetic Energy from source.

• In LATER chapter: Electromagnetic Waves (EM): Radio, TV, Light, etc. These waves carry Photon Energy from source.


Forces and Elastic Materials

• Elastic Material Properties:

• When stretched, the Stretch (which is called Deformation) and the Force are proportional to each other.

• Completely recovers its shape after the deforming force is removed. ( Demo Orange Slinky )

• They can be compressed as well as stretched.

Periodic Motion

Any motion that repeats itself exactly without stopping. The terms used to describe it are in the figure below, which covers periodic motion in general.

The production of sound involves a special periodic motion.


Forces and Vibrations

• Vibration: ( Demo Coil Slinky )

• A Special Periodic Motion. ALL elastic SOLIDS can be made to vibrate.

• Equilibrium Position: ( Demo Coil Slinky On Board )

• Rest Position. Where it would be if not vibrating.

• Displacement, PLUS or MINUS: ( Demo Coil Slinky On Board )

• How far from equilibrium position at any moment.

• Simple Harmonic Motion (SHM):

• A Periodic motion in which the restoring force is opposite and proportional to displacement. Covers a lot of situations. ( Including Elastic Materials )

• DEMO Sinusoidal Curve. ( Fig.5.4 vs time )

• This curve used to graph SHM (Simple Harmonic Motion).


Describing Vibrations

• Amplitude of the Wave: ( Demo WAVE Fig.5.4 )

• The MAXIMUM displacement from Equilibrium Position.

• Cycle: ( Demo Coil Slinky )

• One complete vibration.

• Period of the Wave: ( Demo WAVE Fig.5.4 )

• Time for one cycle.

• Symbol: T, Units: [s].

• Frequency of the Wave: ( Demo Coil Slinky )

• Number of cycles per second.

• Symbol: f, Units: [Hz]. ( Has dimensions of 1/s )

1 1

Thus f TT f


Waves

• A Vibrating Source disturbs its surroundings.

• This disturbance, not the vibrating molecules themselves, travels away from the source. Propagation Speed depends on:

• Wave Type, Mechanical or Electromagnetic and

• Material in which it is propagating.

• The disturbance carries energy away from the source.

• WAVE IS: A traveling disturbance that transports energy.

• Wave energy propagates faster than disturbed "particles" can move.

• Propagation Direction:

• Direction in which wave is traveling.

• Most waves spread out radially from their source.

• Mechanical Wave: (This Chapter)

• Transports KE of Molecular Vibrations away from source.

• Must have molecules (matter) for propagation.


Vibrational Classes of Waves

• Two Major Classes, depending on whether

vibrations are parallel or perpendicular to propagation direction.

• Figure 5.6 on p.127 shows both of these.

CLASS of Mechanical Wave

VIBRATION PHASES OF MATTER

EXAMPLE

Longitudinal Parallel All Sound

Transverse Perpendicular Solid ONLY Taut String

(Combination) Solid, Liquid (Liquid Surface; Earthquake)


Waves in Air (must be Longitudinal) – Are Described by

• Compression: Extra Molecules jammed together.

• This is a better term than "condensation" used in text .

• Rarefaction: Thinned out Molecules.

Hearing Sound Waves in Air

• Source: A Vibration (with KE) starts a wave in surrounding matter.

• These Mechanical Vibrations compress and rarefy the surrounding air.

• This KE propagates outward.

• Waves reach eardrum and set it vibrating at same frequency.

• Normal Human Hearing Range: vibrations from 20 to 20,000 Hz.

• Infrasonic: Below 20 Hz.

• Ultrasonic: Above 20,000 Hz.

• Pitch: The brain's interpretation of sound frequency.


More Terms Describing Waves

• We've already defined: amplitude, cycle, period, and frequency.

• Figures 5.8-A & B (p.129): horizontal axes should be labeled "distance."

• Because these 2 parts show sound waves propagating in air.

• Figure 5.8-C (p.129): horizontal axis should be labeled "time."

• Because this Part shows sound wave vibrating in TIME at a fixed point in space.

• Figure 5.9 (p.129): horizontal axis should be labeled "(propagation) distance."

• Shows a sound wave vibrating in SPACE at a fixed time. ("snapshot")

• Crest: Highest Point. Maximum Compression.

• Trough: Lowest Point. Maximum Rarefaction.

• Wavelength: Distance between two identical wave points.

• Wave Eqn (Derive ?) v f ( v = speed fixed by Wave Type & Material )

• REMEMBER: Sources produce frequency.

Corresponding wavelength is: v

f

• Do Ex. B-14, p.149.


Sound Waves

• Longitudinal wave in which molecules interact in sequence down the line. Thus it needs a "medium" (substance) for its transmission.

• Speed of sound depends on the

• Material of the medium and its

• Physical Conditions, such as temperature.

• Typical Values in Table 5.1, p.124. (Sequence: Gas, Liquid, Solid.)

Speed (Velocity) of Sound in Air

The Text Book has a section on the effect of air temperature on this Speed. While it's interesting, you are NOT responsible for this equation in this course. We'll assume air to be 20ºC (Room Temperature).

Speed of Sound in Air

20Use ONLY : 343

Don't Use 331 0 06

C

T

v m s

v [m s] . T [ C]


Refraction and Reflection

• The concepts in this section, which apply to ALL Wave Types (Mechanical and E-M), are best introduced with Sound. Remember them later on.

• DEMO Point source, a few rays.

• Wavefront:

• As a wave spreads, the parts emitted from the source at same time can always be identified (and marked).

• Smooth curve drawn through these points is called a "wavefront".

• If source is small compared to distance, wavefronts start as spherical.

• As distance gets very large, a sphere gets closer to a flat plane.

These are called Plane Waves.

• Boundary:

• Boundary is the separation between

• different materials or

• different physical conditions in the same material.


• Refraction:

• Occurs because Wave Speed differs across boundary.

• Then different parts of an angled wavefront will travel at different speeds.

• The faster the speed, the further that part travels in each time unit.

• Result is a bending of the path as the wave crosses boundary.

• Reflection:

• Occurs at boundary between different materials.

• Part of the energy is reflected back into the first material,

part passes into the second material, (and may be partly absorbed), and

the rest is Transmitted through.

• Energy in Energy Reflected Absorbed Transmitted .

• Reverberation: (Applies to sound waves only)

• Reflected sound that returns to the ear before 0.1 sec.


Interference

• A PROPERTY OF WAVES (or wave pulses) ONLY (not particles, not even the particles that are vibrating in the wave).

• Waves of the same type can exist in the same place at the same time.

• When they do, the effects of their individual disturbances add algebraically to a new disturbance. See Fig.5.16, p.136:

• As pulses cross the same place, they reinforce Constructively or cancel Destructively.

• After crossing, they have their original shape.

• Destructive Interference between sound waves from 2 or more loudspeakers leads to "dead spots" in the room.

• Beats:

• Fig.5.17, p. 136: The horizontal axis is time.

• Two waves of slightly different frequencies hit a detector.

• The sound gets fainter and louder at the "beat frequency".

• Beat Frequency: 12 fffb

• Musical instruments are "tuned" by listening for zero beats.


Energy and Sound

• The energy per second passing a point in space is the power.

W

t

EP

• Intensity, the power per unit area is what sound meters measure.

]mW[

A

PI

2

Loudness

• The brain's interpretation of the intensity of a sound wave.

• Human ear can hear from 121 10 2I W m to 21 W mI .

• The brain interprets chages in intensity logarithmically.


Loudness (The brain interprets changes in intensity Logarithmically.)

• The scale used is called the "decibel scale". (Table 5.2 on p.137 & Below.)

• 0 dB is at the threshold of hearing.

• each time you multiply the intensity by 10, you add 10 to the dB scale. ( Mult by 100 adds 20, etc.)

• each time you divide the intensity by 10, you subtract 10 from the dB scale. ( Div by 100 subtracts 20 )

Table-5.2


Resonance

• All objects have natural frequencies of vibration that are usually damped (kept from getting large) by internal friction.

• If an object gets energy at a periodic rate matching a natural frequency, the

Amplitude of vibration can get VERY LARGE.

• This is called Resonance.

• Resonant Frequency is another name for natural frequency.

Sources of Sounds

• All sounds have vibrations as their source !!

• Many forces (blows with a hammer, scraping with a bow, etc.) contain a range of frequencies. Only those matching the object's natural frequency resonate and produce sound.

A good example is sound from Vibrating Strings, used not only for stringed musical instruments (next section), but also in our own Larynx.

Another example is air blown into a pipe, which also contains a range of frequencies. Pipe Organs & Wind Instruments select the resonant one. (This subject was dropped from this edition of the text, but see my notes below.)


Vibrating Strings

• Natural Frequencies of a Stretched String:

• Excite a stretched string near one end.

• Wave energy travels to the ends and is reflected back and forth.

• String vibrates at integer multiples of its lowest (fundamental) frequency.

• Interference causes some portions to move a lot, others not at all. See Fig.5.23,p.140.

• The points that do not vibrate are called nodes.

The two fixed ENDS MUST BE NODES.

• The point(s) that vibrate most are called antinodes.

• Each Antinode Length = 1/2 wavelength.


Vibrating Strings (Continued)

• String Natural Frequencies: 1 2 32n

n vf , n , , ,...

L

• n=1 is called fundamental frequency, others are overtones.

• The Fundamental determines each strings Pitch.

• The combined Overtones determine instument's characteristic quality.

• (Extra Information, no questions on this) Designing String Instrument’s Fundamental Frequency:

• Formula for wave speed in string Fundamental Frequency in String

Tension

Linear Densityv . \ 1

1 Tension

2 Linear Densityf

L .


Vibrating Strings (Continued)

• Standing Waves: See Fig.5.22,p.139. (Not really standing, they just look that way)

• (DEMO) Resonance feeds in energy so that antinodes form on string.

• The situation is often called a "Standing Wave", but remember that there really are waves traveling out and reflecting back.

Vibrating Air Columns

• Wind instruments (and organ pipes) also have natural frequencies. The Physics is different from strings in one important way:

• It's AIR that vibrates, so the speed, v = vsound = 343 m/s (at 20°C). Thus the wave speed in instrument is not available for tuning.

• Length of air column (like string length) determines frequencies.


Sounds from Moving Sources

Doppler Effect: occurs with all types of waves. Fig.5.25, p.141.

• ANY Relative motion between observer and wave source changes the detected

(Heard, seen, or measured) frequency.

• approaching each other, frequency is higher ( shorter).

• moving away from each other, frequency is lower ( longer).

• Doppler Effect Uses:

• Radar: Measured frequency shifts of reflected radio waves is accurate enough to determine speeds to less than one mph.

• Astronomy: Light from distant stars is shifted towards lower frequency (moving away). The shift increases with distance. This is strong evidence that the universe is expanding.

Shock Wave: ( Show Demo ) Fig.5.26, p.142.

• If the source is moving AT the speed of sound, the compression crests stay with the source and add up to a very large disturbance creating a Sonic Boom that moves with the source. Faster than speed of sound, Shock Front bends back.

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