What is the speed of a transverse wave in a rope of length 1.50 m and mass 69.0 g under a tension of 500 N?
sqrt(T/(m/L))=sqrt(500/(0.069/1.5))
To determine the speed of a transverse wave in a rope, we need to use the formula:
Speed (v) = √(T/u)
Where:
- Speed (v) is the speed of the wave
- T is the tension in the rope
- u is the linear mass density of the rope
First, we need to calculate the linear mass density (u) of the rope using the formula:
u = m/L
Where:
- m is the mass of the rope
- L is the length of the rope
Given that the length of the rope (L) is 1.50 m and the mass (m) is 69.0 g, we need to convert the mass to kilograms:
m = 69.0 g = 69.0/1000 kg = 0.069 kg
Now we can calculate the linear mass density:
u = 0.069 kg / 1.50 m
Next, we can substitute the values of T and u into the formula for speed:
v = √(500 N / u)
Finally, we can calculate the speed of the transverse wave in the rope.