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This probably doesn't fit into the realm of regular questions ; it is more of an applied rather than theory/math question ...

Anyway, I'm curious whether a metre diameter speaker fitted over a manhole may dislodge any blockage using the principle of resonance. Obviously blockage would be best dislodged at a frequency specific to the blockage. If this silly thought is practicable - would infra-sonic, or ultra-sonic frequencies serve better (as a rule of thumb)?

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I'd be very surprised if a lump of sludge blocking a sewage pipe had any useful resonance.

The idea of using a resonance is that the amplitude of oscillation builds up rapidly in response to the sound. However this will only happen if the oscillation has a high Q i.e. if it doesn't dissipate much energy. For a wine glass this is a good approximation, hence the legendary ability of opera singers to break wine glasses (I think, though I wouldn't swear to it, that this is an urban myth).

I would guess that the gunge blocking your typical sewage pipe will have very high dissipation so you wouldn't be able to build up any significant resonance and therefore the sound will have little effect on it.

If you're interested in pursuing this further, Wikipedia has a good article on resonance. See http://en.wikipedia.org/wiki/Resonance for the details.

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Wouldn't the lengths of the pipe/s resonate ... akin to agitating a bottle when something blocks the flow? – Everyone May 1 '12 at 12:52
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When you agitate a bottle you are causing the contents to oscillate to and fro in the hope that when the moving contents hit the blockage their momentum will break through the blockage. This only works because you're applying a lot of force (with your arm) to shake the bottle. The idea of a resonance is to apply a small force and have this cause a large motion. This only works if the moving object can absorb energy from the sound wave but not dissipate it, so the energy of the moving object builds up and up. Gunge in the pipe would certainly absorb the energy in your sound wave but it ... – John Rennie May 1 '12 at 14:02
... would immediately disspiate it in viscous losses, so you wouldn't be able to build up enough energy to make anything move far. Unless your loudspeaker had as much power as a small bomb it wouldn't have much effect. It would be easier to use a small bomb! – John Rennie May 1 '12 at 14:04
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Use ultrasound at around 40 khz. It is the cavitation frequency for water. That should clean your pipes bare to the metal.

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"Cavitation frequency for water": Could you please share any references about this? Thanks. – Anindo Ghosh Feb 8 at 8:52

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