PhysicsChapter 9: Waves
Intensity of Waves
Explanation level
Overview
Wave intensity is the energy carried per unit area per unit time, or power per unit area. For a progressive wave, intensity is proportional to the square of amplitude.
Learning Outcomes
- Waves transfer energy from one location to another without transporting matter overall.
- Intensity is energy transferred per unit area per unit time.
- Equivalently, intensity is power per unit area: I = PA.
- Since P = Et, intensity is I = EAt.
- The SI unit of intensity is watt per square metre, W m⁻².
- For a progressive wave, I ∝ a², where a is amplitude.
Intermediate Level
Energy Transport by Waves
Sound, water, seismic and electromagnetic waves all transport energy. Their effects depend not only on the total energy but also on how rapidly it arrives and over how large an area it is distributed.
Definition of Intensity
Intensity I measures the rate at which wave energy crosses unit area perpendicular to the direction of travel. If power P passes uniformly through area A:
Power is energy transferred per unit time, P = Et. Substitution gives:
Units and Dimensions
| Quantity | Symbol | SI unit |
|---|---|---|
| intensity | I | W m⁻² |
| power | P | W |
| energy | E | J |
| area | A | m² |
| time | t | s |
Intensity and Amplitude
For a progressive wave in the same medium, intensity is directly proportional to the square of amplitude a.
| Amplitude factor | Intensity factor |
|---|---|
| 2 | 2² = 4 |
| 3 | 3² = 9 |
| 12 | (12)² = 14 |
| √50 | 50 |
Concentration and Spreading
The same power produces a greater intensity when concentrated over a smaller area. A focused beam can burn material, while waves that spread over a growing area become less intense farther from their source.
Textbook Example 9.1: Solar Collector
The average sunlight intensity is 500 W m⁻². Find the energy falling on a 0.50 m² collector in 4.0 h.
I = 500 W m⁻², A = 0.50 m²
t = 4.0 h = 4.0 × 3600 s = 14400 s
E = IAt
E = (500)(0.50)(14400) J
Final answer: E = 3.6 × 10⁶ J
Doubling Amplitude
Explanation: The factor is the square of the amplitude factor.
Required Amplitude Increase
By what factor must amplitude increase to make intensity 50 times larger?
I₂I₁ = (a₂a₁)²
50 = (a₂a₁)²
a₂a₁ = √50
Final answer: Amplitude must increase by √50 ≈ 7.07 times.
Common Mistakes
- Intensity is power divided by area, not power multiplied by area.
- Convert time to seconds when using SI units.
- Doubling amplitude makes intensity four times larger, not twice as large.
- Use the area perpendicular to the direction of energy flow.
Short-Question Preparation
Q. Define wave intensity.
A. The energy carried by a wave per unit area per unit time, or power per unit area.
Q. Write the two intensity equations.
A. I = PA and I = EAt.
Q. State the SI unit of intensity.
A. W m⁻².
Q. How does intensity depend on amplitude?
A. For a progressive wave, intensity is proportional to the square of amplitude: I ∝ a².
Sticky Notes
- Waves transfer energy from one location to another without transporting matter overall.
- Intensity is energy transferred per unit area per unit time.
- Equivalently, intensity is power per unit area: I = PA.
- Since P = Et, intensity is I = EAt.
- The SI unit of intensity is watt per square metre, W m⁻².
- For a progressive wave, I ∝ a², where a is amplitude.
60-Second Revision
Intensity is power per area: I = PA. Since P = Et, I = EAt and E = IAt. Its unit is W m⁻². For progressive waves, I ∝ a², so amplitude changes are squared.
Summary
Wave intensity is the energy carried per unit area per unit time, or power per unit area. For a progressive wave, intensity is proportional to the square of amplitude.
Ask-the-Tutor Modes
- Explain intensity simply.
- Derive I = EAt.
- Solve an energy-transfer numerical.
- Explain the amplitude-square rule.
- Test me with an MCQ.
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Exam preparation
Exam Focus
Important points
- Waves transfer energy from one location to another without transporting matter overall.
- Intensity is energy transferred per unit area per unit time.
- Equivalently, intensity is power per unit area: I = PA.
- Since P = Et, intensity is I = EAt.
- The SI unit of intensity is watt per square metre, W m⁻².
- For a progressive wave, I ∝ a², where a is amplitude.
Common mistakes
- Intensity is power divided by area, not power multiplied by area.
- Convert time to seconds when using SI units.
- Doubling amplitude makes intensity four times larger, not twice as large.
- Use the area perpendicular to the direction of energy flow.
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Intensity of Waves
Sticky Notes · Quick Revision
Key Point 1
- Waves transfer energy from one location to another without transporting matter overall.
Key Point 2
- Intensity is energy transferred per unit area per unit time.
Key Point 3
- Equivalently, intensity is power per unit area: I = PA.
Key Point 4
- Since P = Et, intensity is I = EAt.
Ready to test yourself?
You've completed the learning section.
- 8 concept questions
- Easy → Medium → Hard
- Explanation after each answer
Exam Practice
Important Question
Q1. Define wave intensity.
Important Question
Q2. Write the two intensity equations.
Important Question
Q3. State the SI unit of intensity.
Important Question
Q4. How does intensity depend on amplitude?
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