The intensity level of a sound is reported in unit decibel(dB). how does IL change if we increase a sound intensity by a factor of 10?

a)remains the same
b) increases by 1dB to 2dB
c)it increases by 2dB to 20dB
d)it increases by 20dB to 200dB
e) it decreases

equations...
IL=10(log I- logIo)

..i have posted this before and the person who answered got the same thing I had been getting...that it increases by a factor of ten...this is a textbook question so the answer must be there and our conclusion incorrect..is it possible that they mean the sound intensity, after taking the log of it, is multiplied by 10..and in that case e would be the correct answer?

any help is greatly appreciated.

Say intensity 1 = Io

then intensity 2 = 10 Io

dB1 = 0 dB
dB2 = 10 (log 10 Io - log Io)
which is 10 log 10 = 10
10-0 = 10
We all agree.

I bet the meant the PRESSURE increases by a factor of ten. Then it is 20 log for dB.

To determine how the intensity level (IL) changes when we increase the sound intensity by a factor of 10, we can use the equation IL = 10(log I - log Io), where I is the new sound intensity and Io is the reference intensity.

Let's analyze the possible answers:

a) If the IL remains the same, it would mean that increasing the sound intensity by a factor of 10 has no effect on the IL. This contradicts the equation, so we can eliminate this option.

b) If the IL increases by 1dB to 2dB, it suggests that increasing the sound intensity by a factor of 10 results in a small increase in IL. However, the equation indicates that the change is proportional to the logarithm of the intensity difference, so this option seems unlikely.

c) If the IL increases by 2dB to 20dB, it suggests that increasing the sound intensity by a factor of 10 leads to a significant increase in IL. This could be a conceivable outcome based on the equation.

d) If the IL increases by 20dB to 200dB, it would mean that increasing the sound intensity by a factor of 10 results in a very substantial increase in IL. However, this seems highly unlikely, as the equation indicates a logarithmic relationship.

e) If the IL decreases, it would mean that the intensity level decreases when the sound intensity is increased. This contradicts the equation and is also unlikely.

Given the equation IL = 10(log I - log Io), and considering the logarithmic relationship between sound intensity and IL, the most reasonable answer would be c). Increasing the sound intensity by a factor of 10 would lead to an increase in IL of 2 dB to 20 dB.

It is important to note that the equation you provided relates the IL to the difference in logarithms of sound intensity values, not the direct multiplication of the intensity by 10. Therefore, interpretation of the equation is crucial in understanding the relationship between sound intensity and IL.