Physics · Lesson 12

Point Wave

Wave Mechanics Point Source Circular Wavefronts Amplitude & Distance

Drop a pebble in still water and you have the perfect image of a point wave. A single source sends ripples outward in concentric rings. As they spread, the energy is shared over a growing circumference — so amplitude falls with distance.

What is a Point Wave?

A point wave (or point source wave) originates from a single location and spreads outward equally in all directions. In two dimensions (like water) the wavefronts are circles. In three dimensions (like sound or light) they are spheres.

The key properties of any wave apply: wavelength (λ) is the distance between crests; frequency (f) is how many crests pass per second; wave speed is v = fλ; and amplitude is the height of each crest.

Amplitude vs. distance: In 2D, energy spreads over a circle of circumference 2πr, so amplitude decreases as 1/√r. In 3D it spreads over a sphere of area 4πr², so amplitude decreases as 1/r (and intensity as 1/r²). This is the inverse-square law for intensity.

Interference between two point sources

When two point sources emit waves of the same frequency, their circular wavefronts overlap and interfere. Where crest meets crest — constructive interference — you get a larger amplitude. Where crest meets trough — destructive interference — they cancel out. This is the basis of the famous double-slit experiment.

Simulator

Click anywhere on the canvas to add a wave source (up to 3). Watch the circular wavefronts spread and interfere. Use the panel to adjust frequency and speed.

Sources1

Frequency1.0 Hz

Wavelength—

Click canvas to add source. Click existing source to remove it.

Real-World Applications

💧

Water RipplesA stone dropped in a pond creates a classic point-wave pattern — circular wavefronts expanding outward with decreasing amplitude.

🔊

Sound from a SpeakerA small loudspeaker approximates a point source. Sound pressure waves spread outward, weakening with distance — why you must stand closer to hear quiet music.

📡

Radio TransmittersAn omnidirectional antenna radiates electromagnetic point waves. Signal strength falls as 1/r² — doubling distance quarters the received power.

🌟

StarsLight from a star spreads as a spherical point wave. This is why stars appear dimmer with distance — intensity follows the inverse-square law.

Practice Problems

Easy1. A wave has frequency 5 Hz and speed 20 m/s. What is its wavelength? (λ = v/f)

Hint: λ = 20/5 = 4 m

Easy2. In a point-source wave in 3D, if the distance from the source doubles, the intensity becomes…

Hint: Intensity ∝ 1/r². Double r → 1/4 intensity.

Medium3. Two point sources 0.4 m apart emit waves of wavelength 0.2 m in phase. At a point equidistant from both sources, the waves will…

Hint: Same source, same distance → zero path difference → constructive interference.

Challenge4. A point source of sound has intensity 16 W/m² at 2 m distance. What is the intensity at 8 m? (I ∝ 1/r²)

Hint: r ratio = 4 → intensity ratio = 1/16 → 16/16 = 1 W/m²