Optics & Waves · AP Physics 1 Unit 6 (Simple Harmonic Motion)
Simple Harmonic Motion & Mechanical Wave Simulator
Key exam takeaway: Waves transport energy, not matter! Medium particles oscillate locally around equilibrium and do not travel along with the wave crest.
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3D Simulation Stage● 60 FPS
Parameter Controls
Hz
cm
m/s
Live Derivations & Metrics
Wavelength λ
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Oscillation Period T
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Max Particle Velocity
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Wave Function y(x,t)
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Real-Time Formula Derivation
Governing Formula:
--Substitution:
--Regime: --
Worked Examples & Exam Question Deep Dive
Worked Problem
Problem: Transverse wave travels right at 10m/s with f=5Hz. Find: 1) wavelength and period; 2) particle state after 0.25s starting upward from equilibrium.
Step-by-Step Derivation:
- 1) T = 0.2s, λ = 2m. 2) 0.25s = 1.25T. Starting upward, at 1.25T the particle reaches the crest (v=0, accel negative max).
Worked Problem
Problem: Will a leaf floating on water be carried toward shore by incoming water ripples?
Step-by-Step Derivation:
- No! The leaf oscillates up and down in place. Waves transfer momentum and energy, not bulk mass.
Student Inquiry Worksheet & Practice Problems
Q1. Variant 1: When an SHM oscillator passes equilibrium, what are its displacement, speed, acceleration, and restoring force?
Answer Key: Displacement x=0; restoring force F=0; acceleration a=0; speed reaches absolute maximum (kinetic energy maximum).
Q2. Variant 2: When at maximum displacement (amplitude A), describe displacement, velocity, and acceleration.
Answer Key: Displacement is max (A); restoring force is max toward center; acceleration is max; speed is instantaneously zero.
Q3. Variant 3: When sound enters water from air, which property stays strictly constant? Which change?
Answer Key: Frequency f stays strictly constant (governed solely by the source). Sound speed v increases, so wavelength λ elongates proportionally.
Frequently Asked Questions & Misconceptions
How do vibration graphs (y-t) and wave graphs (y-x) differ?
y-t graph charts the motion history of a single particle over time. y-x graph is an instantaneous snapshot of all spatial particles at one moment.
What is the distinction between transverse and longitudinal waves? Is sound transverse or longitudinal?
Transverse: oscillation perpendicular to propagation (light, string waves). Longitudinal: oscillation parallel to propagation (air acoustic waves).
Why don't particles travel along with the propagating wave?
Particles are tethered by intermolecular elastic restoring forces, compelling them to oscillate around fixed equilibria without gross translation.
What is the superposition principle? Do colliding waves shatter each other?
No! Waves pass through each other independently. In the overlap region, displacements superpose, then separate intact.