Table 6: Table of (approximate) P0 and sound pressure levels in decibels relative to the threshold of human hearing at 10−12 watts/m2 of shock waves, events that produce distorted overpressures greater than one atmosphere. These “sounds” can be quite extreme! The Krakatoa explosion cracked a 1 foot thick concrete wall 300 miles away, was heard 3100 miles away, ejected 4 cubic miles of the earth, and created an audible pressure antinode on the opposite side of the earth. Tambora ejected 36 cubic miles of the earth and was equivalent to a 14 gigaton nuclear explosion (14,000 1 megaton nuclear bombs)!

11.4: Doppler Shift

Everybody has heard the doppler shift in action. It is the rise (or fall) in frequency observed when a source/receiver pair approach (or recede) from one another. In this section we will derive expressions for the doppler shift for moving source and moving receiver.

Figure 134: Waves from a source moving towards a stationary receiver have a foreshortened wavelength because the source moves in to the wave it produces. The key to getting the frequency shift is to recognize that the new (shifted) wavelength is λ′ = λ0 − vsT where T is the unshifted period of the source.

Suppose your receiver (ear) is stationary, while a source of harmonic sound waves at fixed frequency f0 is approaching you. As the waves are emitted by the source they have a fixed wavelength λ0 = va/f0 = vaT and expand spherically from the point where the source was at the time the wavefront was emitted.

However, that point moves in the direction of the receiver. In the time between wavefronts (one period T ) the source moves a distance vsT . The shifted distance between successive wavefronts in the direction of motion (λ′) can easily be determined from an examination of figure 134 above:

We would really like the frequency of the doppler shifted sound. We can easily find this by using