Wave Formulas & Optics
Reference for Mechanical Waves, Acoustics (Sound), and Geometric Optics (Light).
Wave Speed Equation
Period-Frequency
Angular Frequency
Wave Number
Doppler Effect (Approaching)
Doppler Effect (Receding)
Speed of Sound (Solid)
Decibel Level
Snell's Law
Refractive Index
Lens Maker's Formula
Thin Lens Equation
Speed of Waves in Different Media
The Physics of Vibration
Everything vibrates. From the atoms in your body to the light from distant stars, the universe is built on waves. This table bridges the gap between mechanical waves (like Sound) and electromagnetic waves (like Light), providing the tools you need to solve problems in acoustics and optics.
The Doppler Effect
Have you ever noticed how a race car sounds like "Neee-oooow" as it passes? That's the Doppler Effect. As the source approaches, waves bunch up (Higher Pitch / Blue Shift). As it recedes, waves stretch out (Lower Pitch / Red Shift). This same principle helps astronomers measure the speed of galaxies.
Bending Light (Refraction)
Light takes the path of least time. When it enters a denser medium like water or glass, it slows down and changes direction. Snell's Law quantifies this bending, which is the foundational principle behind every camera lens, telescope, and even your own eyes.
Sound vs. Light: Key Differences
| Property | Sound Waves | Light Waves |
|---|---|---|
| Type | Mechanical (Needs Medium) | Electromagnetic (No Medium needed) |
| Direction | Longitudinal (Push/Pull) | Transverse (Up/Down) |
| Speed | ~343 m/s (in Air) | ~300,000,000 m/s (in Vacuum) |
| Behavior | Faster in dense solids (Steel) | Slower in dense solids (Glass) |
The Lens Maker's Equation
Optometrists use this to design glasses. It relates the focal length of a lens to the curvature of its surfaces and the material it is made of.
Positive R is convex, Negative R is concave.
Frequently Asked Questions
What is the Doppler Effect?
The Doppler Effect is the change in frequency of a wave in relation to an observer who is moving relative to the wave source. It explains why a passing ambulance siren sounds higher pitched as it approaches and lower as it drives away.
What is Snell's Law?
Snell's Law describes how light bends (refracts) when passing between two different media, like air and water. Formula: $n_1 \sin(\theta_1) = n_2 \sin(\theta_2)$.
Does sound travel in space?
No. Sound is a mechanical wave, meaning it needs a medium (like air, water, or steel) to travel through. Space is a near-vacuum, so there are no particles to transmit the vibration.
What is the Refractive Index?
The Refractive Index (n) measures how much a material slows down light. It is defined as the ratio of the speed of light in a vacuum to the speed of light in the material ($n = c/v$). Diamond has a high index (~2.42), making it sparkle.
What is the difference between Transverse and Longitudinal waves?
In Transverse waves (like Light), particles oscillate perpendicular to the direction of travel. In Longitudinal waves (like Sound), particles oscillate parallel to the direction of travel (compression and rarefaction).
Why is the sky blue?
Because of Rayleigh Scattering. Blue light has a shorter wavelength and is scattered more strongly by the nitrogen and oxygen molecules in the atmosphere than red light.
What determines the pitch of a sound?
Frequency! A higher frequency corresponds to a higher pitch (treble), while a lower frequency corresponds to a lower pitch (bass).
What is Total Internal Reflection?
It occurs when light tries to move from a denser medium to a rarer one at an angle greater than the "critical angle". The light reflects entirely back inside instead of refracting out. This is how Fiber Optic cables work.
What is the speed of sound in air?
At 20°C (room temperature), the speed of sound is approximately 343 meters per second. It travels faster in warm air and slower in cold air.
What is Resonance?
Resonance happens when an object is forced to vibrate at its natural frequency, causing a dramatic increase in amplitude. This can be used to shatter glass with a voice!