Suppose a normal violin has strings of ~33cm length. The E-string would have a frequency of ~660 Hz.
Let’s shrink that down to tardigrade dimensions (according to Google, it’s about 400μm).
I’m just going to assume the tardigrade violin has a string length of 60μm.
The frequency of strings also depends on tensile stress and mass density - let’s just assume that these scale proportionally.
So we can use the formula: f∝1/L (basically means, half the size means double the frequency).
Let’s calculate the scale factor s for the frequency:
Well well well.
Suppose a normal violin has strings of ~33cm length. The E-string would have a frequency of ~660 Hz. Let’s shrink that down to tardigrade dimensions (according to Google, it’s about 400μm).
I’m just going to assume the tardigrade violin has a string length of 60μm.
The frequency of strings also depends on tensile stress and mass density - let’s just assume that these scale proportionally.
So we can use the formula: f∝1/L (basically means, half the size means double the frequency).
Let’s calculate the scale factor s for the frequency:
L(real) = 330mm, f(real) = 660 Hz L(tardi) = 60μm.
s = L(real) / L(tardi) = 0.33 / 6 * 10⁻⁵ = 5500.
This means that the frequency of the tardigrade E-string would be:
f(tardi) = f(real) * s = f(real) * 5500 = 660Hz * 5500 = 3,630,000Hz = 3.63 megahertz, which is 181.5 times above than the human limit of 20kHz.
Difference in octaves… log2(3.63 Mhz / 660 Hz) = 15.7
That means the tardigade E-string is almost 16 octaves above the human one.