Sound Intensity Formula

Sound intensity is defined as the amount of sound per unit area perpendicular to the route of the sound waves, which is denoted by ‘I’. The standard definition is the measurement of sound energy as a quantity of noise sound intensity in the air at the listener position. The SI unit of sound intensity is watt per square meter (W/m2). 

Formula for Sound Intensity

The sound intensity formula can be defined as the ratio of the power of the sound wave to the area.

I = P/A

where, 

• P = power of the sound
• A = Area

Sample Problems

Problem 1: A person is cheering at a music concert at a  power of 2×10^-4 W. Calculate the sound intensity at a distance of 10m.

Solution:

Given,

• P (power) = 2×10^-4
• A (here distance) = 10 m

So by using the sound intensity formula,

I = P / A

I = 2×10^-4 / 10

I = 2×10^-5

Thus the sound intensity in this condition will be 2×10^-5W/m²

Problem 2: A student at the last bench is 20m away from his teacher and he asks doubt at a sound intensity of 1.1×10^-4. Find at what power he has asked the doubt so that his teacher heard his doubt?

Solution:

Given,

• sound intensity (I): 1.1×10^-4
• Distance (A) : 20m

So by rearranging the formula for sound intensity,

P = I × A

and substituting the values of I and A,

P = 1.1 ×10^-4×20

P = 2.2×10^-3

Thus he has asked the doubt at a power of 2.2×10^-3W

Problem 3: What will be the intensity of the siren of an Ambulance with a power of 8×10^-4 at a distance of 30m?

Solution:

Given,

• power (P) = 8×10^-4
• Distance (A) = 30m

So, according to the sound intensity formula,

I = P / A

I = 8×10^-4×30

I = 0.024

Thus the sound intensity in this condition will be 0.024 W/m²

Problem 4: What will be the distance between two friends in a hall if the one friend calls him at a sound power of 5×10^-4 at 10×10^-4 sound intensity?

Solution:

Given,

• Power (P) = 5×10^-4
• Sound intensity (I) = 10×10^-4

So by rearranging the formula for sound intensity,

A = P / I

and substituting the values of I and P,

A = 5×10^-4 / 10×10^-4

A = 0.5m

Thus the distance between them is 0.5m.

Problem 5: What is the sound intensity of a singer who is singing at a power of 6×10^-4 relative to a person at a distance of 3m.

Solution:

Given,

• Power (P) = 6×10^-4
• Distance (A) = 3×10^-4

So, according to the sound intensity formula,

I = P / A

I = 6×10^-4 / 3

I = 2×10^-4

Thus the sound intensity in this condition will be 2×10^-4 W/m²