Weighted Tuning Forks
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Physics - Waves?
In an experiment on standing waves, a string 47 cm long is attached to the prong of an electrically driven Tuning Fork that oscillates perpendicular to the length of the string at a frequency of 60 Hz. The mass of the string is 0.081 kg. What tension must the string be under (weights are attached to the other end) if it is to oscillate in four loops?
Kia ora
If the string is to move in a standing wave with "four loops" that would be the fourth harmonic, presumably.
So the wavelength will be 0.47/2=0.235m since harmonics occur every time you can fit another half-wavelength into the string.
The frequency is 60Hz so by applying the wave equation v=fλ the wave speed must be 60*0.235=14.1m/s.
The speed of a wave in a string is v=√(T/μ) where T is the tension and μ is the linear density (mass per unit length)
The 0.47m string has mass of 0.081kg so μ=0.081/0.47=0.172kg/m
Rearranging the formula:
T=μv²=34.3N
