Traveling Waves: Crash Course Physics #17

Scientific concepts, discoveries, or nature phenomena presented

Traveling waves on a rope/string

• When you move one end of a rope or string, a disturbance travels through the medium, creating a traveling wave.
• Waves can appear to “disappear” due to interference effects.

General wave formation & propagation

• A wave forms when there is a disturbance in the physical world.
• The information/perturbation spreads outward from the source in all directions (illustrated with examples such as a trampoline).

Key wave parameters

• Peaks/crests and troughs
• Amplitude (A): distance from a peak or trough to the midline
• Wavelength (λ): distance between successive crests (one full cycle)
• Frequency (f): number of cycles passing a point per second
• Wave speed (v):
  • Relationship: v = λ · f
  • Speed depends on the medium, not the wave’s strength (e.g., sound travels differently through air vs. water depending on the medium).

Types of waves (and how they differ)

• Pulse wave
  • Created by moving the rope end back and forth once
  • Example idea: a single crest travels through the rope
• Continuous wave
  • Created by continuously moving the rope end
  • Your hand acts as an oscillator
• Simple harmonic oscillation → sinusoidal waves
  • Sinusoidal wave shape resembles sin(x) when graphed
• Transverse waves
  • Oscillation is perpendicular to the direction of travel
  • Rope example: peaks are perpendicular to the rope’s length
• Longitudinal waves
  • Oscillation is parallel to the direction of travel
  • Described as compression and expansion
  • Examples: springs and sound propagation

Wave energy transport & amplitude-energy relationship

• Waves transport energy through the medium via particle-to-particle interactions.
• For simple harmonic motion, the energy per particle scales as:
  • Energy ∝ A²
  • Doubling amplitude → 4× energy
  • Tripling amplitude → 9× energy

Intensity and how it changes

• Intensity is related to power and area:
  • Intensity = Power / Area
  • Since power is tied to energy transfer (and amplitude affects energy via the square relationship), intensity increases with amplitude according to the square scaling.
• Waves weaken as they spread out due to geometric spreading:
  • For spherical waves, intensity decreases as 1/r²
  • Example:
    • At 2 m, intensity is 4× less than at 1 m
    • At 3 m, intensity is 9× less than at 1 m
  • This helps explain why earthquake effects depend strongly on distance.

Reflection and how boundary conditions affect waves

• Free end reflection
  • A pulse reaches a moving/free ring end and reflects back as a crest (no inversion).
• Fixed end reflection
  • A pulse reflects as a trough (the wave is inverted).
  • Explanation: the rope end can’t move, so the end is effectively yanked downward, inverting the pulse.

Interference (superposition)

• Constructive interference
  • Two identical crest pulses overlap → form a single crest with higher amplitude
• Destructive interference
  • A crest and a trough overlap → the rope appears flat (cancellation)
• Interference applies across wave types (pulse/continuous; transverse/longitudinal).
• Application: noise-canceling headphones
  • They generate sound that destructively interferes with ambient noise.

Earthquake shockwave relevance

• Because intensity depends strongly on amplitude (amplitude squared) and decreases with distance (1/r²), even small changes in distance can greatly affect earthquake damage.

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Lists / methodologies

How wave speed is connected to measurable wave properties

• Wave speed v = wavelength (λ) × frequency (f)

How energy scaling with amplitude is described

• If amplitude changes from A → nA, then:
  • Energy scales as (nA)² = n²A²
• Examples:
  • 2× amplitude → 4× energy
  • 3× amplitude → 9× energy

How intensity changes with distance for spherical waves

• Intensity ∝ 1/r²
• Examples:
  • 2 m: 4× less than at 1 m
  • 3 m: 9× less than at 1 m

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Researchers or sources featured

• Crash Course Physics / Crash Course
• PBS Digital Studios
• Physics Girl
• Shank’s FX
• PBS Space Time
• Doctor Cheryl C. Kinney (Crash Course Studio)
• Thought Cafe (graphics team)