A person listening to music on a stereo system experiences a

A person listening to music on a stereo system experiences a sound level of 70 dB. If the volume dial is turned up to increase the sound intensity by a factor of 500, what sound level would this person hear now?

A. 97dB
B. 105dB
C. 115dB
D. 120dB

Solution

Sol :

If the volume dial is turned up to increase the sound intensity by factor 100 it would increase by 10+10 = 20dB

If the volume dial is turned up to increase the sound intensity by factor 1000 it would increase by 10+10+10 = 30dB

Here we have to add to the initial sound level by

for 100 ------> 100= 10² = 10*10

we have to add 10+10

for 1000 --------> 1000 = 10³ = 10*10*10

we have to add 10+10+10

In the problem sound intensity increases by a factor of 500

500 is in between 100,1000

we have to roughly 10+10+5 = 25dB

final answer 70+25 = 95 dB roughly

In above options, option A is the approximate value, Option A is the correct one.