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Nikolay [14]
3 years ago
11

A particularly beautiful note reaching your ear from a rare stradivarius violin has a wavelength of 39.1 cm. the room is slightl

y warm, so the speed of sound is 344 m/s. part a if the string's linear density is 0.550 g/m and the tension is 160 n , how long is the vibrating section of the violin string?
Physics
1 answer:
raketka [301]3 years ago
8 0
The wavelength of the note is \lambda = 39.1 cm = 0.391 m. Since the speed of the wave is the speed of sound, c=344 m/s, the frequency of the note is
f= \frac{c}{\lambda}=879.8 Hz

Then, we know that the frequency of a vibrating string is related to the tension T of the string and its length L by
f= \frac{1}{2L} \sqrt{ \frac{T}{\mu} }
where \mu=0.550 g/m = 0.550 \cdot 10^{-3} kg/m is the linear mass density of our string.
Using the value of the tension, T=160 N, and the frequency we just found, we can calculate the length of the string, L:
L= \frac{1}{2f}  \sqrt{ \frac{T}{\mu} } =0.31 m
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