Wave Speed Formula
v = fĪ»
Wave Speed Formula
Wave speed equals frequency times wavelength ā always
v = speed (m/s), f = frequency (Hz), Ī» = wavelength (m). Speed is fixed by the medium. Higher frequency ā shorter wavelength.
Doppler Effect
Doppler: toward = higher pitch, away = lower pitch
Doppler Effect
A siren gets higher as it approaches, lower as it recedes
Source moving toward you ā crests bunch up ā higher frequency ā higher pitch. Moving away ā crests spread out ā lower pitch. Used in radar, ultrasound, and astronomy.
Wave Types
Transverse: oscillation perpendicular. Longitudinal: oscillation parallel.
Wave Types
The two fundamental types of mechanical waves
Transverse waves (light, water surface): particles move perpendicular to wave travel. Longitudinal waves (sound): particles compress and rarefy parallel to travel direction. Sound cannot travel through a vacuum ā light can.
Resonance
Resonance: driving frequency matches natural frequency ā amplitude builds
Resonance
Push at the right frequency and things vibrate dramatically
Every object has a natural resonant frequency. Drive it at that frequency ā amplitude grows. Tacoma Narrows Bridge (1940) collapsed due to wind-driven resonance. Basis of MRI, musical instruments, and radio tuning.
Standing Waves
Standing waves: nodes (no movement) + antinodes (max movement). Resonance creates them.
Standing Waves
Standing waves form when reflected waves interfere constructively
A standing wave appears stationary but is really two waves traveling in opposite directions. Nodes: points of zero amplitude. Antinodes: points of maximum amplitude. String instruments and organ pipes use this principle.
Wave Interference
Wave interference: constructive (crests align ā bigger wave). Destructive (crest meets trough ā cancel).
Wave Interference
Two waves overlapping ā they can add up or cancel out
Constructive interference: waves in phase, amplitudes add. Destructive interference: waves out of phase (180Ā°), amplitudes subtract. Superposition principle: resultant wave = sum of individual waves. Beats: two slightly different frequencies ā periodic loud/soft pattern = beat frequency = |fā - fā|.
Sound Intensity and Decibels
Sound intensity: decibels (dB). Every 10 dB increase = 10Ć more intense. 20 dB = 100Ć more intense.
Sound Intensity and Decibels
The logarithmic scale of sound intensity
0 dB: threshold of hearing. 60 dB: normal conversation. 120 dB: threshold of pain. Every 10 dB increase represents a 10-fold increase in intensity. 20 dB increase = 10 Ć 10 = 100Ć more intense. Perceived loudness doubles roughly every 10 dB.
Wave Properties Summary
Frequency determines pitch. Amplitude determines loudness. Speed depends on medium.
Wave Properties Summary
The relationship between frequency, amplitude, and speed
Frequency (Hz): number of complete cycles per second ā determines pitch for sound, color for light. Amplitude: maximum displacement from equilibrium ā determines loudness for sound, brightness for light. Speed: set by the medium ā sound travels faster in solids than liquids than gases.
Electromagnetic Waves
Electromagnetic spectrum: all EM waves travel at c = 3Ć10āø m/s in vacuum. Only speed, not frequency, changes in medium.
Electromagnetic Waves
What all EM waves have in common ā and what distinguishes them
All EM waves: travel at c in vacuum, are transverse, require no medium. Radio waves: lowest frequency, longest wavelength. Gamma rays: highest frequency, most energy. In a medium (glass, water): speed slows, wavelength shortens, but frequency stays the same ā this is why light bends at interfaces.
Diffraction
Diffraction: waves bend around obstacles or through openings. More diffraction when wavelength ā opening size.
Diffraction
Why waves spread out when they pass through gaps
Diffraction is most pronounced when the wavelength is comparable to the opening or obstacle size. Sound diffracts easily around corners (long wavelengths). Light diffracts less visibly (very short wavelength). Single slit and double slit diffraction patterns are classic exam problems.
Resonance in Pipes
Pitch of open pipe: f = v/2L. Closed pipe: f = v/4L. Closed has only odd harmonics.
Resonance in Pipes
Standing waves in air columns ā open vs closed pipes
Open pipe (open both ends): resonates at L = nĪ»/2. Fundamental frequency fā = v/2L. Has all harmonics. Closed pipe (one closed end): resonates at L = nĪ»/4 (odd n only). Fundamental fā = v/4L. Has only odd harmonics (1st, 3rd, 5th...). Flutes are open pipes, clarinets are closed.
Wave Polarization
Polarization: transverse waves can be polarized. Sound waves (longitudinal) cannot be polarized.
Wave Polarization
Why some waves can be polarized and others cannot
Transverse waves oscillate perpendicular to travel ā can be restricted to one plane (polarized). Light can be polarized by filters, reflection, or scattering. Polaroid sunglasses reduce glare by blocking horizontally polarized reflected light. Longitudinal waves (sound) oscillate parallel to travel ā cannot be polarized.