Download PDF by L. I. Sedov, J. R. M. Radok: A course in continuum mechanics Vol. I Basic equations and

By L. I. Sedov, J. R. M. Radok

ISBN-10: 900179680X

ISBN-13: 9789001796808

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Additional info for A course in continuum mechanics Vol. I Basic equations and analytical techniques

Example text

9 × 105 . The decay of a musical sound is part of what gives it its character, and a good musical instrument should have the right Q, but the Q that is considered desirable is different for different instruments. A guitar is meant to keep on sounding for a long time after a string has been plucked, and might have a Q of 1000 or 10000. One of the reasons why a cheap synthesizer sounds so bad is that the sound suddenly cuts off after a key is released. Q of a stereo speaker example 4 Stereo speakers are not supposed to reverberate or “ring” after an electrical signal that stops suddenly.

N / A triangular pulse spreads out. As always, the velocity of a wave depends on the properties of the medium, in this case the string. The properties of the string can be summarized by two variables: the tension, T , and the mass per unit length, µ (Greek letter mu). If we consider the part of the string encompassed by the initial dent as a single object, then this object has a mass of approximately µw (mass/length × length = mass). ) Although the downward acceleration of this segment of the string will be neither constant over time nor uniform across the string, we will pretend that it is constant for the sake of our simple estimate.

Of course, after so many approximations we cannot expect to have gotten all the numerical factors right. The correct result for the velocity of the pulses is v= T µ . The importance of the above derivation lies in the insight it brings —that all pulses move with the same speed — rather than in the details of the numerical result. The reason for our too-high value for the velocity is not hard to guess. It comes from the assumption that the acceleration was constant, when actually the total force on the segment would diminish as it flattened out.

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A course in continuum mechanics Vol. I Basic equations and analytical techniques by L. I. Sedov, J. R. M. Radok

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