Physics 1B: Waves, Sound & Optics

Simple harmonic motion — the atom of oscillation

Simple harmonic motion (SHM) is any periodic motion where the restoring force is directly proportional to the displacement from equilibrium. Two classic examples: a mass on a spring (F = −kx by Hooke's law) and a pendulum swinging through small angles.

Key features of SHM the CBE expects you to know:

• Motion repeats over one period T, measured in seconds.
• Frequency f = 1/T, measured in hertz (Hz = 1/s), tells you how many oscillations per second.
• The pendulum period depends only on length and gravity: T = 2π√(L/g). Mass does NOT affect the period (surprising but true).
• The amplitude (how far from equilibrium) does not affect period or frequency — just the total energy.

Because SHM lies at the heart of every wave, understanding this is not optional. Every particle in a transverse or longitudinal wave undergoes something close to SHM as the wave passes.

Waves — energy in motion

A wave is a disturbance that carries energy from one place to another without transporting matter. When you throw a rock in a pond, the ripples spread outward, but the water molecules themselves stay roughly in place — bobbing up and down, not flowing outward with the ripple.

Two categories:

• Transverse waves — the particles vibrate perpendicular to the wave's direction of travel. Waves on a string, waves on water surface, and all electromagnetic waves (light) are transverse.
• Longitudinal waves — particles vibrate parallel to the direction of travel. Sound waves in air are longitudinal: air molecules compress and rarefy along the direction the sound moves.

Wave properties and the master equation

Every wave is described by four related properties:

• Wavelength (λ) — distance between two consecutive corresponding points (crest to crest, or compression to compression). Units: meters.
• Frequency (f) — how many complete oscillations per second. Units: hertz (Hz).
• Period (T) — time for one complete oscillation. T = 1/f.
• Amplitude — maximum displacement from equilibrium. Determines the wave's energy but not its speed.

These are tied together by the master equation:

v = λ · f

Wave speed depends on the MEDIUM, not on the source. Sound in air at 20°C travels at about 343 m/s regardless of frequency; a higher-pitched sound just has shorter wavelength. Light in vacuum travels at c = 3.00 × 10⁸ m/s regardless of color; blue light just has shorter wavelength than red.

The six wave behaviors

The Physics 1B CBE tests six wave phenomena repeatedly. Learn to identify each in a description or picture.

Reflection

A wave bounces off a boundary. Law of reflection: angle of incidence equals angle of reflection, measured from the normal (perpendicular to the surface). This governs mirror images.

Refraction

A wave bends when it enters a new medium at an angle. The bending occurs because the wave speed changes (light slows down in glass or water). Governed by Snell's law:

n₁ · sin θ₁ = n₂ · sin θ₂

Where n is the index of refraction of each medium. n = 1 for vacuum, ~1.33 for water, ~1.5 for glass, ~2.4 for diamond. A wave going into a denser medium (larger n) bends TOWARD the normal; going into a less-dense medium (smaller n), it bends AWAY from the normal.

Diffraction

A wave spreads out when it passes an obstacle or through an opening. The narrower the opening compared to the wavelength, the more spread. Waves diffract around corners, which is why you can hear a person talking around a door frame even if you cannot see them.

Interference

When two waves overlap, they add. If crests align (in phase), the result is a larger wave — constructive interference. If a crest aligns with a trough (out of phase), they cancel — destructive interference. This produces the alternating bright and dark bands in the classic double-slit experiment.

Resonance

When a driving frequency matches a system's natural frequency, the system's amplitude grows dramatically. This is how you push a swing (timing matters), and why bridges have famously (rarely) collapsed under wind at their resonant frequency.

Doppler effect

The frequency of a wave shifts when the source or observer moves. An ambulance siren rises in pitch as it approaches you (higher frequency because wavefronts are compressed) and drops as it passes (frequency lower because wavefronts stretched). Same physics governs the redshift of distant galaxies in astronomy.

Sound waves

Sound is a longitudinal wave in a fluid or solid. Speed of sound in air at 20°C is approximately 343 m/s. In water, sound is much faster — about 1500 m/s. In steel, faster still — about 5000 m/s. Denser and stiffer materials generally transmit sound faster.

Human ears detect frequencies from roughly 20 Hz to 20 kHz (with high-frequency limit declining as we age). Below 20 Hz is called infrasound; above 20 kHz is called ultrasound. Ultrasound has practical uses: medical imaging (baby ultrasounds), industrial testing, and animal communication.

The electromagnetic spectrum

Light is an electromagnetic wave — an oscillating electric-magnetic field pattern that travels through vacuum at c = 3.00 × 10⁸ m/s. What we call "visible light" is a tiny sliver of a huge spectrum, spanning from radio waves at the low-frequency end to gamma rays at the high-frequency end.

From low to high frequency (equivalently: long to short wavelength):

• Radio waves — meters to kilometers wavelength. AM/FM broadcast, radar, cell phones.
• Microwaves — centimeters. Wi-Fi, ovens, satellite communication.
• Infrared — micrometers. Heat radiation. Night vision.
• Visible light — 400 nm (violet) to 700 nm (red).
• Ultraviolet — hundreds of nanometers. Causes sunburn.
• X-rays — nanometers. Medical imaging.
• Gamma rays — picometers and smaller. Nuclear reactions.

All travel at the same speed c in vacuum. Higher frequency = shorter wavelength = higher photon energy (topic of the next lesson).

Geometric optics — mirrors and lenses

When light hits a smooth reflective surface, it reflects predictably. A plane mirror forms an image the same size as the object, behind the mirror at the same distance the object is in front. The image is upright and left-right reversed.

A thin convex lens converges parallel rays to a focal point at distance f (the focal length) behind the lens. For an object at distance d_o and its image at distance d_i:

1/d_o + 1/d_i = 1/f

Magnification is the ratio of image height to object height:

M = h_i / h_o = d_i / d_o

Positive magnification = upright image; negative = inverted. |M| > 1 = enlarged; |M| < 1 = reduced. If d_i comes out negative, the image is virtual (on the same side as the object, like a magnifying-glass image when the object is closer than f).

Total internal reflection and critical angle

When light goes from a denser medium into a less-dense one at a steep enough angle, it does not refract — it reflects entirely back into the denser medium. The critical angle at which this happens:

θ_c = sin⁻¹(n₂ / n₁)     (where light goes from n₁ to n₂, with n₁ > n₂)

This is the physical principle behind optical fibers: light bounces back and forth inside a thin glass fiber via total internal reflection, transmitting information over kilometers without escaping.

Where students lose points

• Confusing wave speed with frequency. Speed depends on the medium; frequency is set by the source. A siren's pitch (frequency) does not change when it moves from air to water.
• Missing that transverse and longitudinal are different orientations. "The particles vibrate up and down" is transverse; "back and forth along the direction of travel" is longitudinal.
• Applying reflection rule from wrong reference line. Angles are measured from the NORMAL (perpendicular to the surface), not from the surface itself.
• Sign errors in the thin-lens equation. Positive d_o for real object, positive d_i for real image, positive f for converging lens. Sign conventions matter.
• Assuming light travels at c in all materials. Light slows down in matter. c is only its vacuum speed.
• Believing the Doppler effect changes speed. It changes frequency and wavelength, but wave speed remains set by the medium.

Worked example — Snell's law refraction

A ray of light traveling in air (n = 1.00) hits the surface of water (n = 1.33) at an angle of 40° from the normal. Find the angle of refraction in the water.

Step 1 — Snell's law: n₁ sin θ₁ = n₂ sin θ₂.

Step 2 — Plug in: (1.00) sin 40° = (1.33) sin θ₂. sin 40° ≈ 0.643.

Step 3 — Solve: sin θ₂ = 0.643/1.33 ≈ 0.483.

Step 4 — θ₂ ≈ sin⁻¹(0.483) ≈ 28.9°.

Notice the ray bends TOWARD the normal (from 40° to about 29°) because it entered a denser medium (n_water > n_air). This is consistent with the rule stated above.

Check yourself

1. Give a physical example each of a transverse wave and a longitudinal wave.
2. State the master wave equation v = λf and explain each variable.
3. Name and briefly describe the six wave behaviors covered in this lesson.
4. State Snell's law and use it to predict the direction of bending when light enters a denser medium.
5. What is the difference between real and virtual images?
6. A wave has frequency 500 Hz and wavelength 0.68 m. What is its speed?

(Answer to #6: v = λf = 0.68 × 500 = 340 m/s. That is close to the speed of sound in air.)

Practice with CBE-style questions

Waves and optics are heavily tested on the Physics Semester B CBE — nearly a quarter of the questions. Work through the practice bank filtered by Waves, Sound & Optics for questions covering wave properties, interference, refraction, mirrors, and lenses. Every question includes a step-by-step solution.

Independent practice content aligned to Texas Essential Knowledge and Skills (TEKS) §112.39(c)(7). Not affiliated with TTU K-12, UT High School, UT-Austin, the Texas Education Agency, or any Credit by Examination administrator. Texas CBE™ does not administer any exam or grant academic credit.