**Working with Decibels**

Whenever the intensity I is multiplied by a factor of 10, one just adds 10 dB to the value of SL. When the intensity is multiplied by a 100 (10), one must add 20 dB etc. Here are some useful relations:

2.2 Relationship between change in SL and I

There is a relationship between the intensity of a sine sound wave and the value
of the **average pressure oscillation** (p) associated with the wave:

Where,

V = velocity of the sound wave

= the air
density

p = average
pressure oscillation.

For a sine wave,

For normal conditions of temperature and pressure I = 0.00234 x (p) (watt/m). Since according to this relation I is proportional to the square of p () we have

Hence, we can introduce the quality called **sound pressure level (SPL)**:

Funny things seem to happen with the SPL when we superimpose two sounds of the
same frequency and phase. According to the table above, doubling the intensity adds
a mere 3 dB to the sound level of the original sound, whatever the actual value of
the SL might have been. Superimposing *ten* equal tones in phase only increases
the resulting SL by 10 dB.

To raise the SL of a given tone by 1 dB, we must multiply its intensity by 1.26 (or add a tone whose intensity is 0.26 that of the original).

**Appendix A: Intensity/Distance Measurement Examples**

1. If a sound is at an intensity of 0.5 watt/m at 20 metres from the source, what is the intensity at

(a) 10 metres from the source.

(b) 30 metres from the source.

Now x has the same value as (a) above because it is the same source.

2. If a sound is at an intensity of 2 watt/mat 3 metres from the source, what is the intensity at 1 metre from the source.

3. If a sound is at an intensity of 4 watt/m at 2 metres from the source, at what distance is it at an intensity of 0.5 watt/m ?