Waves and Sound

Key Concepts:

Pulses Wave Motion

Types of Waves Standing Waves & Resonance

Sound Doppler Effect

Pulses• A single vibratory disturbance in a medium

• Transverse waves

• Velocity of the pulse• v = √ T/(M/l)• T = tension (N) ; M = mass (kg); l = length (m)

Principle of Superposition• Incidence•

Reflection

Wave Motion• Wave Train – series of waves

• Frequency = f

• (s-1) or Hertz (Hz)

• f = 1/T

• λ= Wavelength (m)• Crests = peaks of a wave• Troughs = valleys of the wave• A = amplitude , maximum displacement up

or down (m)

• Phase = the relative position of a point on a wave

• Intensity (amplitude or volume)• Pitch (frequency)

Types of Waves• Mechanical waves

• Electromagnetic waves

Longitudinal or compression waves

• The vibrations create pressure differences that expand and contract

• Vibrations must be perpendicular to the direction of apparent motion

Polarization

Standing Waves & Resonsance• Fundamental mode

• Standing wave

• Nodal points

λ = 2l

λ = l

λ = 2/3l

λ = 1/2l

Resonance• The build up of wave

energy due to constructive interference

SOUND• Acoustics • acoustical waves

Substance Velocity

Gases (0°)

carbon dioxideAirHelium

259331965

Liquids (25°)

Ethyl alcoholWater, pureWater, sea

120714981531

Solids

LeadWoodIron & steelAluminumGlass (pyrex)

1200-4300-500051005170

• Ultrasonic (>20,000 Hz)

• Loudness = amplitude• Pitch = frequency• Beats = regions of constructive &

destructive interference

Human hearing can detect sound from 20-20,000HZ

• Interference dependent on the path-length difference

• For 2 point sources of sound, A and B:• lA - lB = to a whole multiple of the

wavelength, nλ• Destructive interference will occur if the

path-length = an odd multiple of the half-wavelengths (n+1/2) λ

Diffraction• When a wave

encounters a boundary, it appears to bend around the corners of the boundary

Intensity of sound• Measured in decibels (dB)

• A logarithmic (base 10) system

• l = the intensity in units of watts per square meter• L0 =the barely audible intensity 10-12 watt per square meter

Common decibel measurementsSound Intensity (dB)

WhisperConversationLoud soundDeafening soundPainful soundDamaging sound

306070-90100120140

Doppler effect• As a sound approaches the pitch increases,

as it passes the pitch is decreased• The relationships • are given by

• andv= wave velocity vs= relative velocity of source

• If the source velocity equals the wave velocity, a strong interference pattern builds up in front of the source

• The regions of constructive interference are called shock waves

The ration of the source velocity to the wave velocity is called the MACH NUMBER

• Air Columns

v = λ f = (4L) f1

v= λ f = (4/3L) f3 f3 = ¾ v/L = 3 f1

v= λ f = (4/2L) f2 f2 = ½ v/L = 2 f1

Beats – when 2 waves of the same frequency pass through each other

fbeat = |fb - fb|