In General, Washing machine to the maximum has 1400 rpm during its spin. ie eg: 23 hz. So The sound generated because of this motor is also a comes under the frequency of 23 hz.?
In your case, an electric machines is turning at a given speed and is attached to a solid body, which have its own natural frequencies. Many frequencies will be excited due to the electric motor (you can find many references for this, for example I wrote papers on motor noise and vibrations), excited by electromagnetic and mechanical phenomenas. Thus, you will usually have multiples of the fundamental frequencies + extra frequencies lower and higher. There will, depending on the speed, have particular resonance with the natural frequencies of the objet it is attached to, and you could ear some frequencies much louder than the other.
Hope this is clear, if not, don't hesitate to comment.
Definitely not. Please consider the wave propagation effects. Some (actually all) objects are natural filters, and some are resonators. Fading, echoing and vibrations of washing machine body and parts produce additional noises on many frequencies. Just put a sensor on a surface and check the noise spectrum. 16 bit ADC should be enough.