# Volume of a speaker needed to boil an egg [closed]

I have a fun question to ask that me and my friends couldn't figure out. If I was to boil an egg using a speaker, how loud would that speaker need to be? (Yep, this is clearly what keeps us physicists entertained!) Let's assume the speaker is a distance $$d$$, $$1m$$ away from the egg. I imagine it is quicker to boil the egg not in water, so let's say the egg is placed in front of the speaker. The only thing in the room is the egg and speaker. My extremely approximate solution is as follows: Let the mass of the egg $$m$$ be $$45g$$. The heat capacity $$C$$ of an egg shell is 888 $$J/K kg$$, whereas the white and yolk are more towards $$3500 J/K kg$$. I will assume that the egg has a constant heat capacity of $$3000 J/K kg$$. What equations can we use? We know that the energy, $$Q$$ from heating an object by a temperature change$$\Delta T$$ is , $$Q = m C \Delta T$$ Power $$P$$ can be expressed as $$\frac{Q}{t} = I 4\pi d^2$$, where $$I$$ is the intensity of the sound. The intensity of the sound in Decibels, $$\beta$$, is given as follows, $$\beta = 10\log_{10} (\frac{I}{I_0}),$$ where $$I_0$$ is given as $$10^{-12} W/m^2$$. Plugging all the above in leaves us with, $$\beta = 10\log_{10} (\frac{mC \Delta T}{4\pi d^2I_0t})$$ I like my eggs quite runny, so I will say that $$t = 5min$$. Let's aim to get the temperature of the egg up to $$80$$ degrees celsius from $$20$$ degrees celsius. Inputting all these numbers gives me $$\beta = 123.32 W/m^2$$, approaching that of the volume of a jet engine.

I have made huge assumptions throughout this, and was wondering if anyone had any better ideas on how to accurately calculate the volume needed? For instance, modelling the egg as having one heat capacity is erroneous, and I have not considered sound absorption in the room.

## closed as off-topic by Aaron Stevens, Jon Custer, John Rennie, AccidentalFourierTransform, ZeroTheHeroAug 17 at 13:08

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• First I think you would need to figure out how much sound energy can actually be converted to heating. I feel like a lot of it would dissipate into pressure waves, instead of heat, but maybe that's just a bad assumption on my end. – JMac Aug 15 at 12:54
• I'm completely unqualified to attempt an answer, but I question whether a practical transducer that could do the job would bear any resemblance to something that the average Joe would call a "speaker." – Solomon Slow Aug 15 at 14:55
• Use ultrasound. – David White Aug 15 at 15:01

If you were cooking the egg by actually heating it, then according to your numbers the amount of heat transfer you would need is

$$Q=(0.045kg)(3000\frac{J}{kg^{0} K})(60^{0}K)=8100 J$$

Now according to this MIT website https://engineering.mit.edu/engage/ask-an-engineer/can-sound-be-converted-to-useful-energy/ the roar of a train engine translates to about one hundredth of a watt per square meter.

Assuming a round egg of diameter 2 inches (0.05 m) we have a surface area of 0.03 $$m^2$$. Now assuming the entire surface of the egg absorbs the sound energy of the roaring train engine incident upon it, the energy absorption rate is

$$\dot Q=(0.03 m^2)(0.01 \frac {J}{m^{2}s}) = 0.0003 \frac{J}{s}$$.

This means the time it will take to raise the egg temperature to 80 C will be

$$t=\frac{8100J}{0.0003\frac{J}{s}}=27,000,000s=7500 h$$

If I did my math correctly, unless you can wait 7500 hours to cook your egg, forget about cooking it with your speaker.

Hope this helps.

p.s. Your units for $$C$$ are missing deg K in the denominator

• Awesome, that's really interesting. It's easy to forget the fun problems you can solve with physics. – Pox 219 Aug 16 at 6:50