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 wire, we can use the equation:
v = sqrt(T/μ)
Where:
- v is the speed of the waves,
- T is the tension in the wire,
- μ is the linear mass density of the wire.
First, we need to find the linear mass density of the wire. Linear mass density is defined as mass per unit length:
μ = m/L
Where:
- m is the mass of the wire,
- L is the length of the wire.
Given:
- Length of the wire (L) = 1.0 m
- Mass of the wire (m) = 4.4 g = 0.0044 kg
- Tension in the wire (T) = 650.0 N
Now, we can calculate the linear mass density (μ):
μ = m/L = 0.0044 kg / 1.0 m = 0.0044 kg/m
Next, we can calculate the speed of transverse waves (v):
v = sqrt(T/μ) = sqrt(650.0 N / 0.0044 kg/m) = sqrt(147727.27 m^2/s^2) ≈ 384.08 m/s
Therefore, the speed of transverse waves on the wire is approximately 384.08 m/s.
To calculate the speed of transverse waves on the wire, we can use the equation:
v = sqrt(Tension / (mass per unit length))
where:
- v is the speed of transverse waves
- Tension is the tension in the wire
- mass per unit length is the mass of the wire divided by its length
First, we need to convert the mass of the wire from grams to kilograms:
mass = 4.4 g = 0.0044 kg
Next, we can calculate the mass per unit length:
mass per unit length = mass / length = 0.0044 kg / 1.0 m = 0.0044 kg/m
Now, we can substitute the values into the equation:
v = sqrt(650.0 N / 0.0044 kg/m)
Calculating the square root:
v = sqrt(147727.3 (N * kg/m))
v ≈ 384 m/s
Therefore, the speed of transverse waves on the wire is approximately 384 m/s.