Question

A length of string is stretched between two posts that are 12 m apart. A wave travelling along the string reaches the other end in 1.4 seconds. What is the tension on the string if a 1m length of the string has a mass of 0.2 kg?

Answer 1

Answer 2

To find the tension on the string, we can use the formula:

Tension (T) = (Mass per unit length) × (Wave speed)²

Given: Distance between the posts (d) = 12 m Time taken for the wave to travel (t) = 1.4 seconds Length of the string (L) = 1 m Mass of the string (m) = 0.2 kg

First, we need to find the wave speed. Wave speed is calculated by dividing the distance traveled by the time taken:

Wave speed (v) = Distance / Time = d / t

Wave speed (v) = 12 m / 1.4 s = 8.571 m/s (rounded to 3 decimal places)

Next, we need to find the mass per unit length of the string. Given that a 1m length of the string has a mass of 0.2 kg, the mass per unit length can be calculated as:

Mass per unit length (µ) = Mass / Length = m / L

Mass per unit length (µ) = 0.2 kg / 1 m = 0.2 kg/m

Now, we can calculate the tension on the string:

Tension (T) = (Mass per unit length) × (Wave speed)²

Tension (T) = 0.2 kg/m × (8.571 m/s)²

Tension (T) ≈ 12.77 N

Therefore, the tension on the string is approximately 12.77 Newtons.