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A string with mass density equal to 0. 0025 kg/m is fixed at both ends and at a tension of 290 n. Resonant frequencies are found at 558 Hz and the next one at 744 Hz. The length of the wire will be L = 0.91 m
A resonant frequency of a string is its natural frequency of a standing wave that is produced in it. The standing waves in the string are called harmonics. A string of a fixed length can have many standing waves. The frequencies of these standing waves are called resonant frequencies.
frequency = 1 / 2L ([tex]\sqrt{\frac{T}{mu} }[/tex])
L = length of the spring
T = Tension
fundamental frequency = 744 - 558 = 186 Hz
186 = 1/2(L) ([tex]\sqrt{\frac{290}{0. 0025 } }[/tex])
L = 340 / (186 * 2)
L = 0.91 m
To learn more about resonant frequency here
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