Question

The decibel level of a normal conversation, which has an intensity of watts/m2, is dB. If the decibel level goes up to 80, the intensity of the sound will be watts/m2. Use the formula , where is the sound level in decibels, I is the intensity of sound you are measuring, and is the smallest sound intensity that can be heard by the human ear (roughly equal to watts/m2).

Answer 1

Sound intensity corresponding to 80 dB: $1\cdot 10^{-4}W/m^2$

Step-by-step explanation:

The decibel of a normal conversation is 60 dB, which corresponds to an intensity of $1\cdot 10^{-6} W/m^2$. (1)

The formula to use that relates the intensity of the sound in $W/m^2$ to the sound level in decibel is

$\beta(dB)=10log_{10}(\frac{I}{I_0})$

Where

$\beta$ is the sound level in decibel

$I$ is the intensity

We can found $I_0$ by plugging in the numbers of (1):

$\frac{\beta(dB)}{10}=log_{10}(\frac{I}{I_0})\\\frac{I}{I_0}=10^{\frac{\beta(dB)}{10}}\\I_0 = \frac{I}{10^{\frac{\beta(dB)}{10}}}=\frac{1\cdot 10^{-6} W/m^2}{10^{\frac{60}{10}}}=1\cdot 10^{-12} W/m^2$

Which corresponds to a sound level of 0 decibel.

Now we can find the intensity that corresponds to  a sound level of

$\beta=80 dB$

And from the equation we find:

$I=I_0 10^{\frac{\beta(dB)}{10}}=(1\cdot 10^{-12})10^{\frac{80}{10}}=1\cdot 10^{-4}W/m^2$

Learn more about sound waves:

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