What is the speed of a transverse wave in a rope of length 1.90 m and mass 65.0 g under a tension of 465 N?
To determine the speed of a transverse wave in a rope, we need to use the formula:
v = √(T/μ),
where:
v is the speed of the wave,
T is the tension in the rope, and
μ is the linear mass density of the rope.
First, let's find the linear mass density of the rope. The linear mass density (μ) is given by the formula:
μ = m/l,
where:
m is the mass of the rope, and
l is the length of the rope.
In this case, the mass of the rope is 65.0 g (or 0.065 kg), and the length is 1.90 m. Plugging these values into the formula, we get:
μ = 0.065 kg / 1.90 m.
Now, we can substitute the values of T and μ into the first formula to find the speed of the wave:
v = √(465 N / (0.065 kg / 1.90 m)).
Simplifying further:
v = √(465 N / 0.03421 kg·m⁻¹).
Using a calculator, we can find the square root and find the value of v.