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Energy and power transmitted by waves

Wave motion · Physics

Transverse wave

Interactive 3D

A travelling wave ribbon. Raise the amplitude to make it taller, the frequency to make it faster.

Controls

Drag the sliders or type a value — the simulation updates live.

m
0.1m1m
Hz
0.5Hz3Hz

Study notes

Example: A sound wave travels in air with a speed of 340 m/s. The wave has an amplitude of 2×10⁻⁶ meters and a frequency of 500 Hz. The air density is 1.2 kg/m³. Step 1: Find angular frequency ω = 2πf = 2π×500 = 1000π rad/s. Step 2: Use power formula for sound: P = (πρvA²f²). Plug in values: P = π × 1.2 kg/m³ × 340 m/s × (2×10⁻⁶ m)² × (500 Hz)². Step 3: Calculate (2×10⁻⁶)² = 4×10⁻¹². (500)² = 2.5×10⁵. Step 4: Multiply: π × 1.2 × 340 × 4×10⁻¹² × 2.5×10⁵. Step 5: 1.2×340 = 408. 408×4×10⁻¹² = 1.632×10⁻⁹. 1.632×10⁻⁹ × 2.5×10⁵ = 4.08×10⁻⁴. Step 6: Multiply by π ≈ 3.14 → P ≈ 1.28×10⁻³ watts (about 1.3 milliwatts).

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