Intensity Formula, Definition, Solved Examples

Intensity Formula: Intensity refers to the amount of energy transmitted by a wave per unit time across a unit area of a surface. It is equivalently calculated as the product of energy density and wave speed. Typically expressed in watts per square meter, intensity varies based on the wave's strength and amplitude. Denoted as I, intensity is quantified by the formula:

Intensity = Power / Area

Intensity formula  I =  P/A ​

Here, I represents intensity, P stands for power, and A denotes the cross-sectional area.

Let's consider a few solved examples to better understand intensity calculations:

Intensity Formula Solved Examples

Example 1: Calculate the intensity of a wave with a power of 40 mW and a cross-sectional area of 2 × 1 0 5 mm 2 2×10 5 mm 2 .

Answer: Given values are P=40mW=40×10 −3 W and

A=2×10 5 mm 2 =2×10 −4 m 2 .

Using Intensity Formula :

I=  40×10 −3 ​ / 2×10 −4

I=200W/m 2

Example 2: Determine the power of a wave with an intensity of 8×10 −6 W/cm 2 and a cross-sectional area of 75cm 2 .

Answer: Given values are I=8×10 −6 W/cm 2 and

A=75cm 2 =0.0075m 2 .

Using Intensity Formula : P=I×A

P=8×10 −6 ×0.0075

P=6×10 −8 W

Example 3: Calculate the intensity of a wave with a power of 15 kW 15kW and a cross-sectional area of 25m 2.

Answer: Given values are P=15kW=15×10 3 W and A=25m 2 .

Using Intensity Formula : I= 15×10 3 ​ /  25

I=600W/m 2

Example 4: Determine the power of a wave with an intensity of 5 × 1 0 − 4 W/mm 2 5×10 −4 W/mm 2 and a cross-sectional area of 30 mm 2 30mm 2 .

Answer: Given values are I=5×10 −4 W/mm 2 and

A=30mm 2 =3×10 −5 m 2 .

Using Intensity Formula : P=I×A

P=5×10 −4 ×3×10 −5

P=1.5×10 −8 W

Example 5: Calculate the intensity of a sound wave with a power of 12 mW 12mW and a cross-sectional area of 8cm 2 .

Answer: Given values are P=12mW=12×10 −3 W and

A=8cm 2 =8×10 −4 m 2 .

Using Intensity Formula : I= 12×10 −3 ​/ 8×10 −4

I=15W/m 2

Therefore, the intensity of the sound wave is 15 W/m 2 15W/m 2 .

Example 6: Calculate the power of a laser beam with an intensity of 2.5kW/m 2 and a cross-sectional area of 0.02m 2 .

Answer: Given values are

I=2.5kW/m 2 and A=0.02m 2 .

Using Intensity Formula :

P=I×A  = 2.5 × 1 0 3 × 0.02

P=2.5×10 3 ×0.02

P=50W

Therefore, the power of the laser beam is 50W.

These examples illustrate the application of intensity formulas in different scenarios involving power and cross-sectional area.

Intensity in the context of waves refers to the amount of energy transmitted per unit time across a unit area of a surface. It is a crucial parameter in understanding the strength and impact of waves. The intensity of a wave can be calculated using specific formulas, depending on the given values of power and cross-sectional area.

Intensity Formula 1 (for Power and Area):

I= P ​ / A

Where  I is the intensity,  P is the power, and  A is the cross-sectional area. Intensity Formula  (for Power and Area in different units): I=  P ​/ A This formula is applicable when the power is given in watts and the area is in square meters. Intensity Formula  (for Intensity and Area): P=I×A

This formula is useful when you have the intensity and cross-sectional area. These formulas provide a systematic approach to calculating and understanding the intensity and power of waves in various units. Applying these formulas to given scenarios helps in quantifying and comparing the strength of different waves based on their energy transmission characteristics.

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