Topic 9.111 min read
Intensity of Waves
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.
Choose Your Level
Beginner Level
Intensity tells us how strongly wave energy is delivered to each square metre. Concentrating the same power into a smaller area produces a more intense wave.
Recommended for Class 11
Intensity of Waves
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.
Exam Focus
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.
Important formulas
- I = PA
- I = EAt
- E = IAt
- I ∝ a²
- I₂I₁ = (a₂a₁)²
Common exam traps
- 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.
Long question structure
Definition → derivation from power → unit → amplitude relation → solved numerical.
Common Mistakes
Common Mistakes
- Mistake
Intensity is power divided by area, not power multiplied by area.
- Mistake
Convert time to seconds when using SI units.
- Mistake
Doubling amplitude makes intensity four times larger, not twice as large.
- Mistake
Use the area perpendicular to the direction of energy flow.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
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.
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.
- Definition
- 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.
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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?