Two loudspeakers are being compared. One is perceived to be 32 times louder than the other. The difference in intensity levels between the two, when measured in decibels, is

Step-by-step solution

∆ β = β 2 - β 1 = 10 log I 2 I 0 - 10 log I 1 I 0 = 10 log I 2 I 1 Increasing the intensity by a factor 10 changes the sound level by 10 dB , increasing by 100 changes β by 20 dB . Since, 32 = 2 5 ∆ β = 5 10 = 50 d B