Sound Pressure and Decibels
The sound pressure P for a given sound is given by:
P=10 log WW0
Its units are decibels (dB).
W is the size of a variable energy source (called the sound power), measured in Watts.
Wo is the lowest threshold of sound that humans can typically hear. It is a constant given by:
W0=10−12 W/m2.
The sound pressure is related to the sound intensity of a sound wave. Logarithms are used to cope with the large variation in sound pressure that humans can hear (from the whispering wind at around 20 dB up to the roar of a rock concert at 120 dB, depending on the distance from the speakers).
Exercise 1a
Find the rate of change of the sound pressure P with repect to time if W=7.2 and dWdt=0.5 at some given time t.