A 46-cm-long wire with a mass of 10.5 g is under a tension of 52.0 N. Both ends of the wire are held rigidly while it is plucked.
(a) What is the speed of the waves on the wire?
To find the speed of the waves on the wire, we can use the formula:
v = sqrt(T/μ),
where:
v represents the speed of the waves on the wire,
T represents the tension in the wire, and
μ represents the linear density of the wire.
To find the linear density (μ) of the wire, we need to divide the total mass of the wire by its length:
μ = m/L.
Let's calculate the linear density of the wire first:
μ = m/L = 10.5 g / (46 cm) = 10.5 g / 0.46 m = 22.83 g/m = 0.02283 kg/m.
Now, we can use the formula to calculate the speed of the waves on the wire:
v = sqrt(T/μ) = sqrt(52.0 N / 0.02283 kg/m) ≈ sqrt(2274.29) ≈ 47.7 m/s.
Therefore, the speed of the waves on the wire is approximately 47.7 m/s.