how many decibels is a sound wave produced by a bus that is 10 times as intense as a 50 decibel sound…

Explanation:

Step1: Recall decibel formula

The decibel level $D$ is given by $D = 10\log\left(\frac{I}{I_0}\right)$. Let the intensity of the 50 - decibel sound be $I_1$, so $50=10\log\left(\frac{I_1}{I_0}\right)$. Then $\log\left(\frac{I_1}{I_0}\right)=5$.

Step2: Consider the new intensity

The intensity of the bus sound $I_2 = 10I_1$. The decibel level $D_2$ of the bus sound is $D_2=10\log\left(\frac{I_2}{I_0}\right)=10\log\left(\frac{10I_1}{I_0}\right)$.

Step3: Use logarithm property

Using the property $\log(ab)=\log(a)+\log(b)$, we have $D_2 = 10\left(\log(10)+\log\left(\frac{I_1}{I_0}\right)\right)$. Since $\log(10) = 1$ and $\log\left(\frac{I_1}{I_0}\right)=5$, then $D_2=10(1 + 5)$.

Step4: Calculate the decibel level

$D_2=10\times6=60$.

Answer:

B. 60 dB