Waves, Sound, and Physical Optics

A wave pulse is a single disturbance and a wave is a repeating one; both move energy without moving matter from place to place. Mechanical waves like sound need a medium, while electromagnetic waves don't. In a transverse wave the medium moves perpendicular to the wave's direction; in a longitudinal wave like sound it moves parallel, making compressions and rarefactions. Wave speed depends on the medium, for example $v = \sqrt{F_T/\mu}$ on a string with tension $F_T$ and mass per length μ, and a bigger amplitude means more energy (and a louder sound).

A periodic wave repeats, so you describe it with period T (the time for one cycle), frequency f = 1/T, and wavelength λ (the distance between matching points such as crests). A wave's amplitude is separate from its frequency, and for any periodic wave v = fλ. A graph of displacement versus position is a snapshot of the wave at one moment, while a graph of displacement versus time follows one point of the medium; for sound, higher frequency means higher pitch.

When a wave reaches a boundary between two media, part of it reflects and part is transmitted. The reflected part flips upside down if the wave is entering a medium where it travels more slowly (like a light string tied to a heavy one) and stays upright if it travels faster, and the frequency stays the same either way. Transverse waves, including light, can be polarized so they oscillate in a single plane, which can lower their intensity (power per unit area); longitudinal waves like sound can't be polarized.

An electromagnetic wave is made of electric and magnetic fields that oscillate perpendicular to each other and to the direction the wave travels, so it's transverse. It needs no medium and moves at c = 3.00 × 10⁸ m/s in a vacuum. You should know the spectrum in order of decreasing wavelength (radio, microwave, infrared, visible, ultraviolet, X-rays, gamma rays) and the visible colors from red to violet, but not exact wavelength ranges.

The Doppler effect is the change in observed frequency when a wave source and an observer move relative to each other. When they move toward each other, you measure a higher frequency than the source emits (a higher pitch for sound); when they move apart, you measure a lower one, and a bigger relative speed means a bigger shift. In this course the Doppler effect is qualitative only, so focus on explaining the direction of the shift.

Overlapping waves pass through each other, and at each point the total displacement is the sum of the individual ones (superposition): constructive where they add, destructive where they cancel. Two sounds with slightly different frequencies make beats at $f_{\text{beat}} = \lvert f_1 - f_2 \rvert$. Waves confined to a string or pipe can form standing waves with fixed nodes and antinodes; the longest possible wavelength is the fundamental, and a pipe closed at one end supports only odd harmonics.

Diffraction is the spreading of a wave around an obstacle or through an opening, and it's strongest when the opening is about as wide as the wavelength. Light passing through a single slit of width a makes a wide central bright band with dark bands on either side, which come from wavelets inside the slit interfering. The dark bands sit where a sin θ = mλ, and for small angles you can use the screen distance L to find how far each dark band is from the center.

Light from two narrow slits a distance d apart interferes to make evenly spaced bright fringes where d sin θ = mλ, and for small angles the fringe positions on a screen follow from the same geometry. Young's double-slit experiment was key evidence that light is a wave, and the full pattern is these fringes inside the envelope of single-slit diffraction. A diffraction grating has many evenly spaced slits that make sharper maxima; with white light, the center stays white and each higher order spreads into a rainbow with red farthest out.

In a thin film, light reflecting off the top surface interferes with light reflecting off the bottom surface. A reflection gains a half-wavelength (180°) phase shift when it bounces off a material with a higher index of refraction, but not off a lower one, and refraction never shifts the phase. Film thickness, wavelength and those phase shifts decide whether reflected light is reinforced or canceled, which explains the colors of soap bubbles and oil slicks and how antireflection coatings work. The simplest coating is a quarter of a wavelength thick, measured inside the coating, and calculations use light hitting the film straight on.