Sonic boom and resonance

Can the damage caused by sonic booms be seen as an example of resonance? that is, when the driving frequency (be the sound wave) is equal to the natural frequency of the glass being damaged?

• The frequency content in a sonic boom is pretty broad, so while some resonance may occur, the pressure wave is the more likely source of damage (and it goes from over- to under-pressure rapidly). – Jon Custer Jun 22 '15 at 14:04

If we look at the sonic boom as a $\delta$-function, where we have a really loud sound for a really short time, then it will be able to excite all frequencies at the same way.

You can actually compute this by showing that $$\delta(t)=\frac{1}{2\pi}\sum_n e^{int},$$ which show how the $\delta$-function is actually composed of all frequencies.

Then it's actually in resonance with any object. However, due to its short lifespan it cannot feed more and more energy into an object (like a window), making the amplitude of the oscillation bigger and bigger until the object breaks.

What most likely will destroy something like a window is the actual pressure front, due to the pressure gradient.

No. A sonic boom is an acoustic disturbance caused by supersonic flow over an aircraft's surface. Supersonic flow creates a discontinuous shock boundary that emanates from the aircraft surface and the shock wave propagates behind the aircraft with a large amount of energy, however dispersive as it travels through the atmosphere.

Resonance does require an energy source, but also a 'system' - either a simple object or collection of interacting objects that are capable not only of receiving energy, but also trapping that energy such that it moves about in the system as different forms of energy (for example potential and kinetic).

So while objects on the ground may resonate as they receive energy from a sonic boom, one cannot say that a sonic boom is an 'example' of resonance. It is an example of an energy source that is capable of exciting particular resonant systems.

air is not a medium that is isolated to any object. its can transfer energy over long distance without actaully physically move very long distance. we do not need to separate resonance to a closed system where it only works in the eye of the observers mind. resonance can travel trough air much faster than the air itself. imagine a big container full of air. if you increase the pressure at the core, the whole container will increase pressure all at once because of internal expasion.

if the pressure in the core drop and increse, the whole pressurized volume will experience oscillation even only the center of the container is whats actually change in pressure and quite momentarly. this effect also happend in the atmosphere.

think of the earth atmosphere as if its inside a container and you will understand what happens. the sonic boom causes the expansion wave to create a pressure wave and the immediate drop in the wave as the plane moves, causes the pressure of the expansion wave to travel backwards against the forward moving pressure wave and if the frequency between the two is close enough it causes interference. the system become a resonant system as a whole, even if the volume of the effect is seemingly local.

when two frequencies are to far apart in wavelenght , they don not produce much interference so one wave have to be one half the wavelenght of the other, to cause iterference, as well as what we call a standing wave.

we must realize that the effect in the air is moving in a lot more volume than the plane itself and that its not a problem with the plane itself but with the changes in pressure in th atmosphere locally. actually when a loudspeaker vibrate it actually cause the air to expand and contract almost at the same time or as fast as the frequency of vibration goes that depends on the speed of the air particles.

with a sonic boom, the air particles travel very fast and will oscillate very quickly as the atmospheric pressure pushes back against the traveling wave in a delay. when the plane reaches the speed of sound, the traveling wave and the counter pressure delay can cause the two to become so close in frequency that they clash and causes interference that can create a destructive force in a limited space of the atmosphere.

we need to remeber that the plane is traveling ahead of the speed of sound, but not instantainously, but very fast and when it goes ahead of the sound wave, it the two waves as expansion and contraction will go past each other like below the speed of sound.

its obviosuly a atmospheric phenomena, that is not linked to just the plane alone but involved more than the plane itself.

the study of aerodynamics have been vastly superior than to the study of resonance in varying mediums and therby, the need to involve resonance in any explenation have been unnecessary by aerodynamic experts. resonace is a very powerful effect and caused the tacoma narrow bridge to fall dawn when it hit a certain frequency.

resonance is in need of a deeper study as it will solve many future problems in aerodynamics if we start to look deeper and can definitely explain sonic booms.