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154. Problem 20.48 (RHK) A 30.0-cm violin string with linear mass density
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is
placed near a loudspeaker that is fed by an audio oscillator of variable
frequency. It is found that the string is set into oscillation only at the
frequencies 880 and 1320 Hz as the frequency of the oscillator is
varied continuously over the range 500-1500 Hz. We have to find the
tension in the string.|
Solution: Click For PDF Version Length of the violin string,
Linear mass density of the string,
It is given that the string is set into oscillation the
frequencies 880 Hz and 1320 Hz, when an oscillator is varied continuously over
the frequency range 500-1500 Hz. Let the tension in the string be F. In a
violin ends of its strings are clamped. So we are considering stationary states
in a string with both ends being nodes. For stationary states the wavelength
Frequency at resonance can be found from the speed of sound in the string given by
Let us assume that the two resonant frequencies correspond to
algebraic equation from which can solve for
We use the expression of f given in terms of F, L and n. It is
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and the
length are related as
and
. We then
have an 
.
It is
