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🌊 Waves – JEE Advanced Objective Library

Complete Mechanical Waves objective questions from basic to toughest JEE Advanced level.

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🌊 WAVES (Mechanical Waves)

Stage 3 – Page 8 : Energy, Power & Intensity of Waves (JEE Advanced)

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1️⃣ Energy Transport in Mechanical Waves

Mechanical waves transfer energy without transporting matter. Each particle oscillates about its mean position while energy flows through the medium.

✔ Energy is proportional to the square of amplitude
✔ Higher amplitude → more energy

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2️⃣ Energy of a Stretched String Wave

For a sinusoidal wave on a stretched string:

y = A sin(kx − ωt)

Energy per unit length:

E = (1/2) μ ω² A²

• μ = mass per unit length
• ω = angular frequency
• A = amplitude

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3️⃣ Kinetic & Potential Energy in Waves

At any instant:

• Total energy = KE + PE
• Average KE = Average PE

👉 Maximum KE occurs at mean position
👉 Maximum PE occurs at extreme positions

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4️⃣ Power Transmitted by a Wave

Power is the rate of energy flow through the medium.

P = (1/2) μ ω² A² v

• v = wave speed

✔ Power ∝ A²
✔ Power ∝ ω²

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5️⃣ Intensity of a Wave

Intensity is defined as power transmitted per unit area.

I = P / A

For spherical waves:

I ∝ 1 / r²

⚠ This is known as the Inverse Square Law

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6️⃣ Energy Distribution in Standing Waves

• No net energy transfer
• Energy oscillates between KE and PE
• Nodes have zero energy
• Antinodes have maximum energy

👉 Standing waves store energy locally

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7️⃣ Effect of Medium Properties

• Higher density → lower wave speed
• Higher tension → higher energy flow
• Amplitude remains unchanged unless damping occurs

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8️⃣ Decibel Scale (Sound Intensity)

Sound intensity level:

β = 10 log₁₀ (I / I₀)

• I₀ = 10⁻¹² W/m²

✔ Increase of 10 dB → intensity becomes 10 times

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9️⃣ JEE Advanced Traps

• Assuming energy ∝ amplitude (instead of A²)
• Confusing power with intensity
• Forgetting inverse square law
• Ignoring angular frequency (ω)

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🔟 Final Takeaway

✔ Energy ∝ A² ω²
✔ Power depends on medium + wave parameters
✔ Standing waves do NOT transport energy

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Stage 3 – Page 8 Completed Successfully ✅