Chapter - 2

Key Words: Sound intensity, Acoustic power, Wave energy

Sound Intensity

🎯 Learning Objectives:

In the section, we will look at sound intensity as the last of the sound measurement metrics in the physical domain and compare it to sound power and sound pressure. The real advantage of sound intensity is its property of directionality, and we will see how the spatial location of sound sources can be isolated with sound intensity using heat maps. Finally, we will take a look at the decibel unit of sound intensity level and where its usefulness lies.

With acoustic intensity, we cover the tri-factor of acoustic sound measurements in the physical domain. The other two are sound pressure and sound power which we have we have already covered before. So it should not come as a surprise to you when I state that acoustic intensity can be expressed as some physical unit of measure and can also be expressed in decibel similar to the others. The figure below show this tri-factor representation of these fundamental acoustics quantities.

Signal domain illustration
Figure 1. Signal domains: physical, analog, and digital.

To understand more though let us look at the definition it states that:

An acoustic intensity or sound intensity is defined as the flow of sound energy per second carried by the sound waves per unit area in a direction perpendicular to that area

So there is the flow of sound energy per second which is actually just sound power, which immediately confirms that intensity is a power quantity and not a field quantity. This gives us a lot of intuition about what it could be. And the power carried by sound waves is per unit area, so intensity is power over area or in derived units that would be watt per meter squared and finally the direction of this sound wave is perpendicular to the area. I=PowerArea(Wm2)I=\frac{Power}{Area}(\frac{W}{m^2}). So the sound intensity is a directional quantity and represents the direction of propagation of the sound wave. This is a unique attribute that differentiates intensity from sound pressure and sound power. The other two are non-directional and it does not give us any indication of where a particular source of sound is located. But in other aspects sound intensity shares similar properties as power and pressure.

Just like pressure sound intensity changes based on the distance from the source. The further away you are from the source the lesser the sound intensity at a cross-sectional area of space. And just like sound power intensity is a calculated value. It needs a fairly controlled and complex setup to measure and calculate the values.
This is explained in the figure below.

Signal domain illustration
Figure 1. Signal domains: physical, analog, and digital.

Let us consider a source vibrating and resonating in a free field, meaning that there is no obstacles to the path of the sound waves in a three-dimensional space and the energy of the sound waves are not absorbed into its surroundings. It is quite obvious to note that these sort of spaces are incredibly hard to emulate in the real world but hypothetically let us say that this exists A sound wave emanating from this source always has a sphere of influence the sound waves travel upwards in all directions similar to how a ripple originates in still water, when a pebble is thrown in. But just imagine that in three dimensional space. So when we want to calculate the intensity of sound across a certain area of space the area needs to be either a part of the surface area of the sphere or it could be the surface area of the entire sphere. Calculating sound intensity across the entire sphere of influence is quite easy. We just need to know the sound power of the source and the distance we are from the source. The distance from the source will essentially become the radius of the sphere and we can mathematically calculate the surface area of the sphere with the formula 4πr2.
Hence the sound intensity can be calculated as,

I=P4πr2I=\frac{P}{4πr^2}

So we can also notice that intensity is inversely proportional to the square of the distance from the source. Intensity follows the inverse square law where intensity decreases exponentially, the further away we are from the source. Contrast that the sound pressure, the pressure drops linearly, the further away you are from the source. This is illustrated in the following Figure.

Signal domain illustration
Figure 7. Signal domains: physical, analog, and digital.

Let us say we calculate the sound intensity at a meter away from the source a certain cross-sectional area of space. The sound intensity here represents the of the sound flowing through this patch. As the sound wave travels further at two meters from the source, the sound energy those once flowing through that patch is now flowing through a larger area of space, more precisely four times larger than before. The energy is merely redistributed to a larger area of space, so the intensity drops by four. Similarly at three meters from the source the intensity drops by nine. So we can see that the intensity is inversely proportional to the square of the distance.
We can visualize why intensity drops exponentially with the help of the following animation.

🧪 Interactive Examples

Dual-Source Water Wave Interference 3D

Heatmap of interference with circular wavefronts propagating from two sources.

📝 Key Takeaways

  • Sound intensity is the flow of sound energy per second per unit area in a direction perpendicular to that area.
  • Intensity is a directional quantity, unlike sound pressure and sound power, which are non-directional.
  • Intensity can be expressed in physical units (W/m²) or in decibels similar to other acoustic quantities.
  • Like sound pressure, intensity decreases with distance from the source; specifically, it follows the inverse-square law.
  • Sound intensity allows for localizing sound sources, e.g., using heat maps, which is not possible with pressure or power alone.
  • Measuring intensity requires a controlled setup, making it more complex than measuring sound pressure.
  • Understanding intensity complements the tri-factor of sound measurements: pressure, power, and intensity.
  • The directionality of intensity helps in analyzing acoustic energy propagation in 3D spaces.
  • Sound intensity can be calculated from sound power and distance, using the formula I = P / (4πr²).
  • Visualization (animations or heat maps) helps to intuitively understand how intensity decreases with distance.

🧠 Quick Quiz

Test your understanding - select and submit an answer.

1) What physical quantity does sound intensity represent?

2) Which property makes sound intensity unique compared to sound pressure and sound power?

3) In which units is sound intensity commonly expressed?

4) How does sound intensity change as the distance from the source doubles?

5) Which law describes the drop in intensity with distance?

6) Which acoustic measurement is non-directional?

7) What additional advantage does measuring sound intensity provide?

8) Which of the following is required to accurately measure sound intensity?

9) Sound intensity is directly related to which other sound measurement?

10) Why is the tri-factor (pressure, power, intensity) important in acoustics?