Question

Approximately how many times louder is a 150-dB sound than a 70-dB sound?

Answer 1

Answer:

$10^{8} times$

Explanation:

Sound intensity level in terms of dB is define by the formula in terms of intensity I as,

$\beta=10log_{10}\frac{I}{I_{0} }$

Given that, the sound levels are given as,

$\beta_{1}=70dB$ and

$\beta_{2}=150dB$

Therefore,

$\beta_{2}-\beta_{1}=10log_{10}\frac{I_{2} }{I_{0} }-10log_{10}\frac{I_{1} }{I_{0} }\\\beta_{2}-\beta_{1}=10log_{10}\frac{I_{2} }{I_{1} }$

Put the values of all variables in the above equation,

$150dB-70dB=10log_{10}\frac{I_{2} }{I_{1} }\\log_{10}\frac{I_{2} }{I_{1} }=\frac{80}{10}\\ \frac{I_{2} }{I_{1} }=10^{8}\\I_{2}=10^{8} I_{1}$

Therefore the 150 dB is $10^{8}$ times louder than 70 dB sound.