How does a 50 decibel sound compare to a 40 decibel sound?

Question

1. 50 decibel is 1/10 as loud as 40 decibel
2. 50 decibel is 1/2 as loud as 40 decibel
3. 50 decibel is twice as loud as 40 decibel
4. 50 decibel is 10 times as loud as 40 decibel

Answer 1

The intensity of sound in decibels is defined as 10 log(I/I_o) where I/I_o is the ratio of the sound's power in watts/m² to the intensity of the human threshold of hearing.

To determine the relative loudness of a 50 decibel sound to 40 decibel sound, calculate the I/I_o for each decibel level and divide the results.

So for 50 db, I/I_o = 100000 and for 40 db I/I_o = 10000. The ratio is 10, so the correct answer is that 50 db sound is 10 times as loud as the 40 db sound.