I am writing a paper that mentions sound at the DNA scale.
What do you think could be the shortest wavelength for sound in water, theoretically?
Could the sound of 2 nm wavelength propagate through water?
2nm wavelength in water corresponds to 750 GHz frequency.
The wavelength of audible sound in water is between 7 cm to 75 m.
The speed of sound is around 1540 m/s in seawater. The wavelengths are related to frequency like this: L = c/f = 1540/f
Sound is pressure waves that animals or humans can hear. For humans that range is about 20 Hz to 20kHz, corresponding to wavelengths from 77 m to 0,077 m under water.
2 nm wavelength is about 200-300/th of the valvelength of visible light. That is: electromagnetic waves.
However acoustic waves in crystals might have short wavelengths like that. Or just the thermal movement of the atoms. However that is a speculation.
I think waves in crystals can interact with light and change the transmission, scattering and absorption of electromacneic waves. To be able to do so they need to be of the same order of magnitude or a little smaller than the light they should interact with.
You could do it in terms of absorption. The absorption coefficient typically follows a frequency squared rule. In water it's 8.1E-15 Np s^2/m * f^2. So at 750 gigahertz that's 4.6 x 10^9 1/m. So lets say you're 1 micrometer from the source then the signal will be attenuated by e^(4.6 x 10^9 x 10^-6) = a very very large number. So no I don't think that's possible.