A 130 cm length of string has a mass of 3.94 g. It is stretched with a tension of 8.60 N between fixed supports. What is the wave speed for this string?
To find the wave speed for this string, we need to use the formula:
wave speed (v) = √(tension (T) / linear density (μ))
Where:
- tension (T) is the force acting on the string (given as 8.60 N)
- linear density (μ) is the mass per unit length of the string
To find the linear density (μ), we need to divide the mass (m) of the string by its length (L):
linear density (μ) = mass (m) / length (L)
Given data:
- mass (m) = 3.94 g
- length (L) = 130 cm = 1.3 m
First, let's convert the mass from grams to kilograms:
mass (m) = 3.94 g = 0.00394 kg
Now, we can calculate the linear density:
linear density (μ) = 0.00394 kg / 1.3 m
= 0.00303 kg/m
Substituting the values of tension (T) and linear density (μ) into the wave speed formula:
wave speed (v) = √(8.60 N / 0.00303 kg/m)
By performing the calculation, the wave speed for this string is:
wave speed (v) ≈ 96.62 m/s