A steel piano wire, of length 1.0 m and mass 4.4 g is stretched under a tension of 650.0 N. What is the speed of transverse waves on the wire?
To find the speed of transverse waves on the steel piano wire, we can use the formula:
v = √(T/μ)
Where:
v is the speed of the transverse waves,
T is the tension in the wire, and
μ is the linear mass density of the wire.
First, let's calculate the linear mass density of the wire, which is the mass per unit length. We can do this by dividing the mass of the wire by its length:
μ = m / L
Given:
Length of the wire (L) = 1.0 m,
Mass of the wire (m) = 4.4 g = 0.0044 kg
Calculating the linear mass density:
μ = 0.0044 kg / 1.0 m
μ = 0.0044 kg/m
Now, we can substitute the values into the formula:
v = √(T/μ)
v = √(650.0 N / 0.0044 kg/m)
Calculating the speed of transverse waves:
v = √(650.0 / 0.0044) m/s
v ≈ 512.3 m/s
Therefore, the speed of transverse waves on the steel piano wire is approximately 512.3 m/s.