Answer: To find the mass of the string, we can use the formula for wave speed in a string, which relates tension (T), mass per unit length (μ), and wave speed (v) as follows:
Wave speed (v) = √(T / μ)
where:
v = wave speed in m/s
T = tension in N
μ = mass per unit length in kg/m
We are given:
Wave speed (v) = 300 m/s
Tension (T) = 240 N
Now, we need to find the mass per unit length (μ) of the string. Rearrange the formula to solve for μ:
μ = T / v^2
Substitute the given values:
μ = 240 N / (300 m/s)^2
μ = 240 N / 90000 m^2/s^2
μ ≈ 0.00266667 kg/m
The mass per unit length (μ) of the string is approximately 0.00266667 kg/m.
To find the mass (m) of the entire 2.5 m long string, we can use the formula:
Mass (m) = μ * Length
m = 0.00266667 kg/m * 2.5 m
m ≈ 0.00666667 kg
The mass of the 2.5 m long string is approximately 0.00666667 kg, which is approximately 6.67 grams.