# Intensity of Sound

One factor that influences loudness can be analyzed objectively, This factor is called sound intensity.** In this post, we will study the definition, concepts, and formula or equation of sound intensity. Then we will solve a sample numerical problem based on the sound intensity equation.**

**Definition**

Sound intensity is a measure of the power of a sound per unit area. Since power is the rate at which energy is received, intensity could also be defined as (energy/time)/(unit area).The SI unit of sound intensity is watts per square meter or W/m^{2}.

**Concepts of Sound Intensity**

As we get farther from the source of a sound, the loudness we perceive becomes less. To relate this to sound intensity, consider an “ideal” situation in which a point source of sound is sending out sound waves in all directions and there are no barriers from which these waves can reflect.

At a certain distance, r, from the source, the energy is spread out over a sphere of surface area **4 Π r ^{2}**. If this distance is doubled to 2r, the surface area of the sphere becomes

**4 Π**

**(2r)**, which is

^{2}**4**times as large.

Thus, the power per unit area reaching the larger sphere is 1/4 as much as at the smaller sphere. Similarly, if the distance becomes 3r, the area is **4 Π (3r) ^{2}**, which is 9 times as large. Thus, the power per unit area reaching the larger sphere is 1/9 as much as at the smaller sphere.

**Sound Intensity Equation**

This typical inverse square relationship between sound intensity and distance can be expressed mathematically as follows:

I ∝ (1/r^{2})

IntensityIis directly proportional to (1/r^{2}) whereIis the intensity in watts per square meter and r is the distance in meters from the source of the sound

**Sample Numerical Problem**

Question: **At a distance of 59 m from a jet taking off, the intensity of the sound is 0.10 W/m ^{2}. At what distance will the intensity be 1/10 of this value? (Neglect the effects of the reflection of sound off the ground.)**

**Solution**:

Using this relation: I ∝ (1/r^{2})I_{1}∝ (1/r_{1}^{2})I_{2}∝ (1/r_{2}^{2})

I_{2}/I= (_{1}r/r_{1}^{2}_{2}^{2})

=>r=_{2}(r_{1}/I_{1}I)_{2}^{1/2}

=>r= (59) (0.1/0.01)_{2}^{1/2}= 59x 10^{1/2}= 59×3.16 = 186 m

At 186 m distance, the intensity. (Answer)willbe 1/10 of the initial value