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)
• λ= Wavelength (m)• Crests = peaks of a wave• Troughs = valleys of the wave• A = amplitude , maximum displacement up
or down (m)
Longitudinal or compression waves
• The vibrations create pressure differences that expand and contract
• Vibrations must be perpendicular to the direction of apparent motion
Standing Waves & Resonsance• Fundamental mode
• Standing wave
• Nodal points
λ = 2l
λ = l
λ = 2/3l
λ = 1/2l
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
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