Sinusoidal signal as density

Question

I produce a magnetic field with a current source and a long cylindrical coil. A current of \$\hat{x}\$ (peak value) with frequency \$f_{x}\$ produces a magnetic field of \$B\$ (RMS value in Tesla) with frequency \$f_{x}\$ that I can measure with a magnetic flux field sensor, e.g. a Hall-sensor, or a fluxgate sensor. When I read the analogue signal with some A/D-card, I can plot the spectrum, which should give me a peak at frequency \$f_{x}\$ and amplitude \$B\$ with the unit Tesla plus some system noise. With some mathematics, I can calculate the spectral density of the spectrum which has the unit T/\$\sqrt{\text{Hz}}\$. Now my question:

Question: What is the physical interpretation of a sinusoidal signal per sqrtHz?

For noise one has to consider the ENBW so it makes sense. For a sinusoidal signal, noise and bandwidth do not fit in the context for me. For the transformation one of course needs to consider resolution bandwidth and window type which determines the ENBW used for the conversion. But does that have physical meaning? As a matter of fact, it is not possible to plot a RMS signal and noise over frequency at the same time, because they have different units.

Answer 1

For a sinusoidal signal, noise and bandwidth do not fit in the context for me.

Nor for anybody else. Since a pure sine wave has zero bandwidth, the signal power over any finite bandwidth is independent of bandwith. That is, a 1 watt signal will have a 1 watt power for any non-zero measurement bandwidth.

So root-hz simply doesn't apply.

As you have realized, it works fine for noise, where the amount of signal varies with bandwidth.