Question

How much more intense is a 90 db hair dryer than 60 db street traffic?

Answer 1

`"90 dB"` is thousand times more intense than `"60 dB"`

Explanation:

Decibel level and intensity are related as

`"dB" = 10 log("I"/"I"_0)`

Where

• `"I ="` Intensity of sound
• `"I"_0 =` Threshold intensity of least audible sound a human can hear

`"dB"_1 = 10log("I"_1/"I"_0)`

`"dB"_2 = 10log("I"_2/"I"_0)`

Subtract second equation from first

`"dB"_1 - "dB"_2 = 10log("I"_1/"I"_0) - 10log("I"_2/"I"_0)`

`"dB"_1 - "dB"_2 = 10log("I"_1/"I"_2)`

`log("I"_1/"I"_2) = ("dB"_1 - "dB"_2)/10`

`color(blue)("I"_1/"I"_2 = 10^(("dB"_1 - "dB"_2)/10))`

Plug in the values

`"I"_1/"I"_2 = 10^((90 - 60)/10) = 10^(30/10) = 10^3`

`∴ "I"_1 = "1000 I"_2`