Question

While the decibel scale can be used in many disciplines, we shall restrict our attention to its use in acoustics, specifically its use in measuring the intensity level of sound. The Sound Intensity Level (measured in decibels) of a sound intensity (measured in watts per square meter) is given by Compute Damage to your hearing can start with short term exposure to sound levels around 115 decibels. What intensity is needed to produce this level

Answer 1

Answer:

I = 0.316 W/m^2

Explanation:

In order to calculate the intensity required to produce a sound level of 115 decibels, you use the following formula:

$B=10log(\frac{I}{I_o})$   (1)

B: sound level = 115dB

I: intensity of the sound = ?

Io: Threshold of hearing = 10^-12 W/m^2

You solve the equation (1) for I, by using properties of logarithms:

$B=log(\frac{I}{I_o})^{10}\\\\10^{B}=10^{log(\frac{I}{I_o})^{10}}\\\\10^B=(\frac{I}{I_o})^{10}\\\\I=I_o10^{B/10}$

Finally, you replace the values of all parameters:

$I=(10^{-12}W/m^2)10^{115/10}\\\\I=0.316\frac{W}{m^2}$

The intensity that produces a sound level of 115 dB is 0.316 W/m^2