Decibel Level: β = 10 log( )I 0 is the threshold of hearing and is equal to 10−12 watts. Note that, while β is
measured in decibels (dB), it is dimensionless.
A useful fact to remember is that if a sound increases by 10 dB, the intensity
increases by a factor of 10.
- How many times more intense is an 82 dB sound than a 52 dB
sound?
Here’s How to Crack It
82 dB is 30 dB louder than 52 dB. Each change of 10 dB increases the intensity by
a factor of 10. 30 dB is 3 × 10 so the intensity would be 10 × 10 × 10 = 1,000 times
more intense.
Beats
If two sound waves whose frequencies are close but not identical interfere, the
resulting sound modulates in amplitude, becoming loud, then soft, then loud, then
soft. This is due to the fact that as the individual waves travel, they are in phase,
then out of phase, then in phase again, and so on. Therefore, by superposition, the
waves interfere constructively, then destructively, then constructively. When the
waves interfere constructively, the amplitude increases, and the sound is loud;
when the waves interfere destructively, the amplitude decreases, and the sound is
soft. Each time the waves interfere constructively, producing an increase in sound
level, we say that a beat has occurred. The number of beats per second, known as
the beat frequency, is equal to the difference between the frequencies of the two
combining sound waves.
fbeat = |f 1 − f 2 |