Question

A train whistle has a sound intensity level of 70. dB, and a library has a sound intensity level of about 40. dB. How many times greater is the sound intensity of the train whistle than that of the library?

Answer 1

The sound intensity of train is 1000 times greater than that of the library.

Step-by-step explanation:

We have expression for sound intensity level,

`L=10log_(10)\left ( (I)/(I_0)\right )`

A train whistle has a sound intensity level of 70 dB

We have

`70=10log_(10)\left ( (I_1)/(I_0)\right )`

A library has a sound intensity level of about 40 dB

We also have

`40=10log_(10)\left ( (I_2)/(I_0)\right )`

Dividing both equations

`(70)/(40)=(10log_(10)\left ( (I_1)/(I_0)\right ))/(10log_(10)\left ( (I_2)/(I_0)\right ))\\\\(7)/(4)=(log_(10)\left ( (I_1)/(I_0)\right ))/(log_(10)\left ( (I_2)/(I_0)\right ))\\\\10^7(I_2)/(I_0)=10^4(I_1)/(I_0)\\\\(I_1)/(I_2)=10^3=1000`

The sound intensity of train is 1000 times greater than that of the library.