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1D Wave Equation

βˆ‚Β²u/βˆ‚tΒ² = cΒ² Β· βˆ‚Β²u/βˆ‚xΒ²
c = 1.00 m/s
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A = 1.00
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Ξ» = β€”
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f = β€” Hz
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T = β€” s
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n = 1
u(x,t) = AΒ·sin(kx βˆ’ Ο‰t)
Kinetic (cyan) Β· Potential (orange) Β· Total (green)
Wave Speed c 1.0
Amplitude A 1.0
Mode n 1
Time Speed 1.0Γ—

Transversal vs Longitudinal

Transversal
displacement βŠ₯ propagation
light Β· string Β· S-wave
Longitudinal
displacement βˆ₯ propagation
sound Β· P-wave Β· spring

🎯 Node Hunt

Harmonic n:
Tolerance:
Score 0
|
Round 1
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Nodes to find β€”
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Taps 0
πŸ‘† Tap where you think the nodes are (points of zero displacement)

2D Wave Equation

βˆ‚Β²u/βˆ‚tΒ² = cΒ² Β· (βˆ‚Β²u/βˆ‚xΒ² + βˆ‚Β²u/βˆ‚yΒ²)
c = 1.00 m/s
|
A = 1.00
|
f = β€” Hz
|
T = β€” s
|
(nx,ny) = 1,1
u(x,y,t) = AΒ·sin(kxΒ·x + kyΒ·y βˆ’ Ο‰t)
βˆ’A
+A
Cross-section along y = 0.5 (dashed line on map above)
Wave Speed c 1.0
Amplitude A 1.0
Mode nx 1
Mode ny 1
Time Speed 1.0Γ—

2D Transversal vs Longitudinal

Transversal (ripple)
displacement βŠ₯ propagation plane
water surface Β· membrane
Longitudinal (compression)
particles oscillate radially, βˆ₯ propagation
sound in a gas

🎯 2D Node Hunt

nx: ny:
Tolerance:
Score 0
|
Round 1
|
Nodal lines to find β€”
|
Taps 0
πŸ‘† Tap on the lines you think never move (nodal lines of the membrane)

3D Wave Equation

βˆ‚Β²u/βˆ‚tΒ² = cΒ² Β· (βˆ‚Β²u/βˆ‚xΒ² + βˆ‚Β²u/βˆ‚yΒ²)
c = 1.00 m/s
|
A = 1.00
|
f = β€” Hz
|
T = β€” s
|
(nx,ny) = 1,1
u(x,y,t) = AΒ·sin(kxΒ·x + kyΒ·y βˆ’ Ο‰t)
drag to rotate Β· scroll / pinch to zoom
Wave Speed c 1.0
Amplitude A 1.0
Mode nx 1
Mode ny 1
Time Speed 1.0Γ—

3D Transversal vs Longitudinal

Transversal
particles oscillate βŠ₯ to propagation
light Β· string Β· S-wave
Longitudinal
particles oscillate βˆ₯ to propagation
sound Β· P-wave Β· spring

🎯 3D Node Hunt

nx: ny:
Tolerance:
Score 0
|
Round 1
|
Nodal lines to find β€”
|
Taps 0
πŸ‘† Click on the surface where you think the nodal lines are (drag empty space to rotate)