Waves and Sound Key Concepts: Pulses Wave Motion Types of WavesStanding 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 SubstanceVelocity Gases (0°) carbon dioxide Air Helium Liquids (25°) Ethyl alcohol Water, pure Water, sea Solids Lead Wood Iron & steel Aluminum Glass (pyrex)

Ultrasonic (>20,000 Hz) Loudness = amplitude Pitch = frequency Beats = regions of constructive & destructive interference Human hearing can detect sound from ,000HZ

Interference dependent on the path-length difference For 2 point sources of sound, A and B: l A - l B = 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 L 0 =the barely audible intensity watt per square meter

Common decibel measurements SoundIntensity (dB) Whisper Conversation Loud sound Deafening sound Painful sound Damaging sound

Doppler effect As a sound approaches the pitch increases, as it passes the pitch is decreased The relationships are given by and v= wave velocity v s = 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) f 1 v= λ f = (4/3L) f 3  f 3 = ¾ v/L = 3 f 1 v= λ f = (4/2L) f 2  f 2 = ½ v/L = 2 f 1

Beats – when 2 waves of the same frequency pass through each other f beat = |f b - f b |