Waves and Sound PHYS 1090 Unit 7
Features of a Wave crest trough Crest: high point Trough: low point Wavelength: crest-crest distance (m) crest Period: crest-crest-timing (s) Here we define names for wave features so that we can communicate easily. l trough
Features of a Wave Amplitude A: (crest height – trough height) / 2 Frequency f: repeats in a given time (cyc/s = Hz) Velocity u: speed of crest motion (m/s) Here we define names for wave features so that we can communicate easily. u A
Relations between Features Period T = 1 / f ; Frequency f = 1 / T Velocity u = l / T = lf Wavelength l = uT = u / f Frequency f = u / l; Period T = l / u
Types of Waves Motion of the medium is perpendicular to the direction the wave travels: transverse wave (example: string wave) Motion of the medium is parallel to the direction the wave travels: longitudinal wave (examples: sound wave, slinky wave) Animation Crest and trough of a longitudinal wave: moving regions of highest and lowest pressure or density. Amplitude of a longitudinal wave: Half the total change in pressure or density
Combining Waves
Adding Waves Together result 3 –3 Run at: W1 = 0.2; k1 = 0.2; ampl = 15 integral multiples (half, third, quarter) of lambda: multiply W1, k1 by 2, 3, 4 add same-lambda wave with negative amplitude Beats: slightly vary w2 and k2 together from wave 1 values Standing waves (use phase velocity of 0.5: k = 2*w) result –3
Wave Interference Constructive: Sum of waves has increased amplitude Destructive: Sum of waves has decreased amplitude Two-wave simulation
Beats Waves of similar frequency combine to give alternating times of constructive and destructive interference
Standing Waves Add a wave to an identical wave traveling in the opposite direction (Its reflection) Medium vibrates, but waves don’t travel Nodes: positions of zero variation Antinodes: positions of maximum variation
Two-Dimensional Waves Ocean waves, earthquake surface waves Wave types animations Membrane standing waves animations
Water Waves Restoring force is gravity Fastest in deep water, slow in shallow water Breaking and refractive behavior in shallow water Speed depends on wavelength Very complicated behavior!
Shoaling and Breaking Waves slow in shallows by shore Wavelength shortens and amplitude rises Troughs move slower than crests Crests fall forward
Wave refraction u = 1/2 u = 3/4 u = 1
Ocean Wave Refraction
2-D Wave Interference interference patterns http://www.falstad.com/ripple/