Answer :
Final answer:
The tension in the wire can be calculated using the wave speed formula and the given parameters. The linear mass density of the wire is first calculated using the given mass and length, and then this is substituted into the formula that relates tension, wave speed, and linear mass density, yielding a tension of approximately 1696 N.
Explanation:
The tension in a string or wire can be calculated using the formula for the wave speed on a stretched string:
v = sqrt(T/μ)
where v is the wave speed, T is the tension, and μ is the linear mass density. In this case, we are given the mass and length of the wire, so we can calculate μ:
μ = mass/length = 0.05 kg / 0.83 m = 0.06024 kg/m.
We also know that the wave speed can be calculated from the frequency and the wavelength. Since we’re dealing with the fundamental frequency here, the wavelength is twice the length of the string, so v = frequency * wavelength = 101 Hz * 2 * 0.83 m = 167.66 m/s.
Now we can substitute our values for v and μ into the equation for wave speed and solve for T:
T = μ * v² = 0.06024 kg/m * (167.66 m/s)² = 1696.29 N.
So the tension in the wire is approximately 1696 N.
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