1. Sound Intensity Level – Learning Outcomes
HL: Define sound intensity and give its unit.
HL: Solve problems about sound intensity.
Define threshold of hearing and frequency response of the human ear.
Give some examples of sound intensity level.
HL: Convert changes in sound intensity to changes in sound intensity level.
Discuss hearing impairment and ear protection.
Describe the dB(A) scale.
Use a sound level meter.

2. HL: Sound Intensity
The sound intensity at a point is the rate at which sound energy is passing through a unit area at right angles to the direction in which the sound is travelling.
Formula: 𝐼= 𝑃 𝐴
𝐼=𝑠𝑜𝑢𝑛𝑑 𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦, 𝑃=𝑝𝑜𝑤𝑒𝑟, 𝐴=𝑎𝑟𝑒𝑎
It is measured in watts per square metre (W m-2).
Sound spreads out in a sphere, so the total area at a given distance is 4𝜋 𝑟 2 (surface area of a sphere).
This also implies that sound intensity has an inverse square relationship with distance:
𝐼∝ 1 𝑟 2

3. HL: Sound Intensity
e.g. What is the sound intensity of a 50 W speaker at a distance of 10 m?
e.g. A foghorn has a sound intensity of 0.5 W m-2 at a distance of 100 m. What is its power rating?
e.g. The sound intensity of a wind turbine 150 m away is about 3×10-8 W m-2. What is its sound intensity at 75 m?

4. Frequency Response of the Ear
The ear is not like a microphone – it picks up some sounds easier than others.
Certain frequencies sound louder than others at the same sound intensity.
The ear is particularly sensitive to sounds in the 2000 to 4000 Hz frequency range.
by Lindosland – public domain

5. Threshold of Hearing Human ears cannot detect all sound.
A minimum sound intensity is required.
Due to the frequency response of the ear, this minimum intensity varies with frequency.
The threshold of hearing is the smallest sound intensity detectable by the average human ear at a frequency of 1 kHz. Its value is 1×10-12 W m-2.

6. Sound Intensity Level
Our ears do not detect differences in sound intensity linearly (e.g. a sound which doubles in intensity does not sound twice as loud).
The highest sound intensity we can safely hear is about times as intense as the lowest.
Thus, we often use a logarithmic scale to represent sound intensity, called sound intensity level.
Logarithmic scales represent factors as linear differences.
In the case of sound intensity, a factor of 10 W m-2 is represented as a difference of 10 deciBels (dB).

7. Sound Intensity Level Noise Sound Intensity Level Threshold of hearing
0 dB
Whisper
20 dB
Suburban estate
50 dB
Conversation
60 dB
Car
70 dB
Lorry
80 dB
Jackhammer
100 dB
Rock concert
110 dB
Threshold of pain
130 dB

8. HL: Sound Intensity Level
A doubling in sound intensity corresponds to a sound intensity level increase of 3 dB. Likewise, halving the sound intensity reduces the sound intensity level by 3 dB.
e.g. the sound intensity of a loudspeaker doubles as a person approaches it. What is the increase in sound intensity level?
e.g. the sound intensity at a concert increases from 85 dB to 94 dB when the concert begins. By what factor has the sound intensity increased?

9. Hearing Impairment
We have previously discussed noise pollution, but we need to look at hearing impairment in detail.
Exposure to sounds above a certain level can permanently damage hearing over time.
Health and safety regulations usually require a maximum exposure to sound levels without ear protection.
Ear protection is required for longer periods.
Sound Level (dB)
Max. Hours per Day 90 8 93 4 96 2 99 1
102
105

10. dB(A) Scale
Due to the frequency response of the human ear, the dB scale does not accurately reflect how loud sounds are.
e.g. a 50 dB sound will appear louder at 2 kHz than at 50 Hz, because our ears are more sensitive to 2 kHz sounds.
The dB(A) scale takes this into account so that 50 dB has the same loudness to our ears regardless of the frequency.

11. dB(A) Scale
by Lindosland – public domain

12. Sound Level Meter
Sound level meters are devices used to measure sound intensity level.
They use a microphone to pick up sound, then display a deciBel value, usually on the dB(A) scale.
Thus, they take the frequency response of the ear into account.
by Harke – public domain