Question

You move closer to the stage so that the (power) intensity of the sound is 500 times greater. What is the change in decibels

Answer 1

Answer: When the power intensity of a sound increases, the change in decibels can be calculated using the logarithmic formula for sound intensity:

Step-by-step explanation:

Change in decibels (dB) = 10 * log10(I2/I1)

where I2 is the new intensity and I1 is the original intensity.

In this case, the sound intensity increases by a factor of 500, so I2 = 500 * I1.

Plugging this into the formula, we get:

Change in decibels (dB) = 10 * log10(500 * I1/I1)

Simplifying further:

Change in decibels (dB) = 10 * log10(500)

Using a calculator, the logarithm of 500 is approximately 2.7.

Therefore, the change in decibels is:

Change in decibels (dB) = 10 * 2.7

Change in decibels (dB) = 27

So, the change in decibels is 27 dB when the power intensity of the sound is 500 times greater.