Final answer:
The equation for relative intensity in dB is β (dB) = 10 × log10(I/Io). It shows that each 10-fold increase in intensity corresponds to an increase of 10 dB. Thus, a 30 dB increase translates to a 1000 times rise in intensity, and doubling the intensity increases the sound level by about 3 dB.
Step-by-step explanation:
The equation for calculating relative intensity in decibels (dB) is given as β (dB) = 10 × log10(I/Io), where β represents the sound intensity level in decibels, I is the intensity of the sound in question, and Io is the reference intensity, typically the lowest audible sound intensity for humans. This equation is founded on the principle that a change in power by a factor of 10 corresponds to a change in level of 10 dB. Hence, if an intensity level is increased by 10 times, this represents an increase of 10 dB. For instance, a sound with a 90 dB intensity level is 30 dB greater than a sound with a 60 dB level, implying that the former is 10³ or 1000 times as intense as the latter. Moreover, if a sound's intensity is 107 times another, it will be 70 dB higher. It's also important to note that a sound intensity level that is twice as intense as another will have a difference of approximately 3 dB.