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The frequency of a signal is hard to change. Some ways that you can change it: reflect it off a moving object change the distance between source and receiver as a function of time (Doppler shift) introduce some non-linear amplification - this will generate harmonics If you just add "noise" (uncorrelated to the signal), you can create constructive or ...

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Typically not. Changing the frequency requires some non-linear process and background noise is simply additive. There potential exceptions: the noise could be so loud that the air and/or the microphone become non-linear, the noise mechanically couples to the string and/or the instrument in a way that changes the resonant behavior, the noise is somehow ...

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I would think the vibrations to be mindful of would include any type of propulsion, thrusters, etc, also any internal electrical motors, actuators, power supplies, etc. Moreover, I would also think essentially anything electrical-related e.g. wiring, capacitors, etc since electrical parts are known to vibrate when current is passing through them. I'm ...

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Extending the other answers to see how "noise averages" are used elsewhere in the book as well, we can think of "noise average" of a dynamical variable ${\bf A}({\bf x},t)$ as $\langle {\bf A}({\bf x},t) \rangle_{noise} = \int_\Omega {\bf A}({\bf x},t) \rho({\pmb \epsilon}) d{\pmb \epsilon}$ where ${\pmb \epsilon}$ is a random noise distributed as ...

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