Question

Regarding the decibel rating system for sounds, every 20 decibels has the effect of increasing the sound pressure by a factor of ________?

Answer 1

Final Answer;

Every 20 decibels has the effect of increasing the sound pressure by a factor of 10.

Step-by-step explanation:

The decibel (dB) scale is logarithmic, and it measures the intensity or pressure level of a sound. The relationship between decibels and sound pressure is expressed by the formula:

`\[ P2/P1 = 10^((ΔL/20)) \]`

where P1 and P2 are the initial and final sound pressures, and ΔL is the change in decibels. For the given question, ΔL is 20 decibels, so the formula becomes:

`\[ P2/P1 = 10^((20/20)) \]`

Simplifying this, we get:

P2/P1 = 10¹ = 10

Therefore, every 20 decibels corresponds to a tenfold increase in sound pressure. This is a fundamental aspect of the logarithmic nature of the decibel scale. For example, if a sound is measured at 60 decibels, it has 10 times the sound pressure of a 40-decibel sound.

Understanding this relationship is crucial in assessing the potential impact and risk associated with varying sound levels, especially in fields such as occupational health and safety or environmental noise monitoring.