Question

Two violin strings each have a length of 0.32 m and are each under a tension of 51 N. The lighter string has a mass density of 6.43x10^-4 kg/m, whereas the heavier string has a mass density of 2.48x10^-3 kg/m. (Note, for stringed instruments, both ends of the string are fixed.)
(a) What are the fundamental frequencies of the (i) lighter and (ii) heavier violin strings?
(b) These strings are plucked simultaneously in such a way that the fundamental of the lighter string and the second harmonic of the heavier string are excited. What beat frequency is heard due to the interference between these modes of the two strings? Also, draw what the excited standing waves look like for (i) the fundamental of the lighter string and (ii) the second harmonic of the heavier string.
(c) If the maximum intensity of the beats is 60 dB 1.0-meters-away from the violin, what is the maximum intensity (in dB) of the beats perceived by an observer 3.0-meters-away from the violin assuming no dissipation? You may treat the violin as a point source, so that the surface area of the spreading wave is 4 π r 2where r is the distance from the source.
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Answer 1

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