4

For sympathetic vibrations, the main frequency will be the driving frequency, but non-linearities will also couple the sympathetic vibrations into vibrational modes with other frequencies as well... but these other modes will in general have frequencies that are not multiples of the driving frequency so they will not resonate and will be minimal (ie, much ...


2

As very well J Thomas states, beats are not perceived as sound. They are perceived as a periodically repeating amplitude variation. This does not define the beat as sound but does define it as a perceivable variation in (at least) one parameter of a sound (in practice there's some small variation in frequency but it is not easily perceived and for most ...


1

There's rolling going on here. Assuming no slipping, you have $\tau = R mg\sin\theta\implies I\alpha = fR$ where $f$ is friction. Since $a=\alpha R$ then you have $$C mR^2 \dfrac \alpha R = fR\implies Cma=f$$ where $I=CmR^2$. Then by Newton's second Law, $$ma=mg\sin\theta-kx-f\implies ma=mg\sin\theta-kx-Cma$$ Then use the chain rule $a=\dfrac {dv}{dt}=\dfrac{...


1

To your first question the answer is yes, you can excite individual modes of a string. It is easy to experience this by plucking a guitar string at different locations while enforcing a node by touching the string lightly at a point where a node is expected for a mode that you want to excite. With a little practice, you can excite at least the first 5 or 6 ...


1

20 hertz gives you a sound that you can probably hear as a tone. 2 hertz gives you a series of beats. It doesn't sound like a tone. If you beat a bass drum twice a second it won't sound like a musical note, but you can hear it.


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