Question

Sound is measured in decibels, using the formula d=10log(p/p0) where p is the intensity of the sound and p0 is the weakest sound the human ear can hear. A horn has a decibel warning of 20. how many times more intense is this horn compared to the weakest sound heard to the human ear?

Answer 1

Solving the given logarithmic equation, it is found that the horn is 100 times more intense compared to the weakest sound heard to the human ear.

What is the equation for the sound in decibels?

The equation is given by:

$d = 10\log{\frac{p}{p_0}}$

In which:

• d is the intensity of the sound in decibels.

• p is the intensity of the sound.

• $p_0$ is the weakest sound that the human ear can hear.

In this problem, we have that d = 20, and we have to solve the logarithmic equation for p to find how many times more intense the sound is:

$d = 10\log{\frac{p}{p_0}}$

$20 = 10\log{\frac{p}{p_0}}$

$\log{\frac{p}{p_0}} = 2$

The logarithm is inverse of the function $10^x$, hence we apply the function to both sides to find the ratio.

$\frac{p}{p_0} = 10^2$

$\frac{p}{p_0} = 100$

Hence, the horn is 100 times more intense compared to the weakest sound heard to the human ear.

More can be learned about logarithmic equations at brainly.com/question/236421

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