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I am planning to make a device that will catch a tennis ball using sound waves to slow down its motion, and make it levitate. But how strong should the sound waves be? Please tell me if there are other specifications than the frequency that I should worry about.

Ex. Details : i Force = That of a weakly thrown baseball perhaps. ii By strong, I mean how much power is required or what frequency is necessary to push the ball and hold it mid air. iii. The device generating these sound waves is a hand-held one.

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  • $\begingroup$ More details? How fast is the ball going to be moving? How are you defining "strong"? $\endgroup$
    – fertilizerspike
    Commented Nov 5, 2022 at 17:42
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    $\begingroup$ The ball is, suppose, thrown by somebody with little force. And strong, I mean how much power should the sound waves carry, like what frequency should it be? $\endgroup$
    – Excaliburx25
    Commented Nov 5, 2022 at 17:43
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    $\begingroup$ Well you're talking about very loud sound, in excess of 150dB. Frequency? I'm out of my depth there but there is lots of literature on the subject. Are you planning on doing this on a tabletop? I would advise not doing that. It could be extremely dangerous and disturbing to neighbors. $\endgroup$
    – fertilizerspike
    Commented Nov 5, 2022 at 17:50
  • $\begingroup$ Not a tabletop, I was actually planning to make a hand-held device... I guessed it would be loud enough to burst my eardrums, but I'm curious. $\endgroup$
    – Excaliburx25
    Commented Nov 5, 2022 at 17:53
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    $\begingroup$ Or fracture your metacarpals... $\endgroup$
    – fertilizerspike
    Commented Nov 5, 2022 at 17:58

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This is utterly, utterly implausible. Let's do an order of magnitude estimate to see why.

The overpressure involved in a sound wave is related to its decibel level by $$ L_p = 20 \log_{10} \left( \frac{p}{p_0} \right) $$ where $p_0 = 20$ micropascals. So let's suppose that you use a 100-dB sound wave (which is about as loud as a car horn at a distance of about 15 feet, and would cause hearing damage after about 15 minutes of exposure. Solving the above equation, we find that a 100-dB sound wave corresponds to overpressure of about 2 pascals, or 2 newtons per square meter, or 0.0002 newtons per square centimeter.

A 5-cm-diameter ball has a cross-sectional area of 20 square centimeters. So the best you could hope for, using sound waves that would damage your hearing, would be a force of about 0.004 newtons. Any object that could be levitated by this sound wave would have to have a weight of less than this. Since $g \approx 10^{-2}$ newtons per gram, any object with a mass above 0.4 grams would be too heavy for a sound wave to levitate.

(This is ignoring the fact that a sound wave is also an oscillating phenomenon, and if the force on the object from the sound wave was upwards one moment it would be downwards the next.)

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    $\begingroup$ Nothing stops us from ramping the "volume" up to 200dB and more, though. Chemical fuels and explosives can do that easily. The heaviest objects man tends to "levitate" this way are planes, helicopters, rockets and artillery shells. Whether that still meets your definition of "sound" is, of course, a matter of taste. $\endgroup$
    – FlatterMann
    Commented Nov 5, 2022 at 23:19
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    $\begingroup$ Is this video consistent with this math? The polystyrene ball is much less dense than a tennis ball, and I don't see the volume given, but at least it looks like unprotected phalanges survive when exposed to the sound. $\endgroup$
    – Mike Serfas
    Commented Nov 5, 2022 at 23:19
  • $\begingroup$ @MikeSerfas : The diameter of the polystyrene ball is 50 mm (according to pure.hw.ac.uk/ws/portalfiles/portal/10765644/… ), whereas the diameter of a tennis ball is about 67 mm. The maximum acoustic pressure in the article is about 8000 Pa, it's about 172 dB. $\endgroup$
    – akhmeteli
    Commented Nov 6, 2022 at 14:01
  • $\begingroup$ Ultrasonic Suspension Technology zs-handling.com/index.php/en Using a vibration generator with separate power electronics, a compressed air film with repulsive forces is generated. In combination with attractive forces, e.g. with negative pressure, handling without contact is also possible from above. $\endgroup$
    – HolgerFiedler
    Commented Nov 7, 2022 at 4:51
  • $\begingroup$ @akhmeteli: Further to your point, note that the decibel scale is logarithmic, so a sound level that is 70 decibels higher corresponds to a pressure level that is 3000 times greater. $\endgroup$
    – Michael Seifert
    Commented Nov 7, 2022 at 15:02
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Not quite what you describe, as it is not quite "sound", but you can use an air blower (or maybe your vacuum cleaner can be reversed). For example, according to the data sheet of a $129 cordless handheld air blower (chosen at random), the blowing force is 10N, much more than the weight of a tennis ball (about 0.56N), so you can choose a cheaper blower.

What is important, the tennis ball will be stably levitated in an upward directed air flow of the blower due to the Bernoulli effect.

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  • $\begingroup$ that would be sound at $\omega = 0 \rm{Hz}$ $\endgroup$
    – hyportnex
    Commented Nov 5, 2022 at 23:58
  • $\begingroup$ @hyportnex : Moreover, it is 79 dB, according to the data sheet :-) $\endgroup$
    – akhmeteli
    Commented Nov 6, 2022 at 0:52
  • $\begingroup$ I was actually hoping to make one using air 'waves'. Like, sound is actually movement of air, so instead of Bernoulli effect I was hoping for something else. $\endgroup$
    – Excaliburx25
    Commented Nov 6, 2022 at 7:13

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