Question

6. There are two main ways to describe how loud a sound is. One is that you can describe its intensity, I, measured in W/m2, which is the amount of energy per unit time, per unit area, transported by the sound. However, this is not very close to the human experience of sound loudness. The human experience of loudness (actually like the way most of our senses work) is that each factor of 10 in intensity sounds like the same sized “step” in loudness. In other words, in our experience of sound, the difference between 0.01 W/m2 and 0.1 W/m2, seems the same as the difference between 0.1 W/m2 and 1 W/m2. For this reason, when talking about loudness we often use the “decibel scale”, defined by

   ?I? β = (10dB)log I0

   where I is the sound intensity, I0 is a reference intensity and β is the loudness in decibels. A common choice for I0 is the “threshold of hearing”, which for a typical person is I0 = 1 × 10−12 W/m2.

   1. (a) What intensity corresponds to β = 0 dB? Does 0 dB mean “no sound”?

   2. (b) The “threshold of pain” (hopefully the name makes it clear what this means...) is 130 dB. What sound intensity

      does this correspond to?

   3. (c) Some sound has a loudness of 50 dB. Another sound has 1200 times the intensity of the first sound. What is the loudness of the second sound?

Answer 1