Question

Find the kinetic energy of pulse travelling in a taut
string. Given T = 10 N and u = 0.1 kg/m.​

Answer 1

Answer:

just put values✌️✌️✌️✌️

hope it help

Explanation:

The kinetic energy will exist within a small section of the string only and it is transverse. There is no longitudinal kinetic energy in a perfect transverse wave.

The amount of kinetic energy depends on the shape of the wave and the amplitude of the wave

Answer 2

The kinetic energy of pulse travelling in a taut  string is 0.15 mJ

Explanation:

At the given time, y = m₁ ⇒ x₀ < x < 0.1 m

After 't' time, y = m₂x + c ⇒ 0.1 m < x < 0.15 m

The mass m₁ is given as:

m₁ = 10⁻³/0.1 = 10⁻² kg

The mass m₂ is given as:

m₂ = 10⁻³/0.05 = 2 × 10⁻² kg

The kinetic energy is given as:

dK = 1/2 dmV²

dK = 1/2 μ.dx (-V. ∂y/∂x)²

∫dK = 1/2 μ.V² [m₁² $\int_{0}^{0.1}$ dx + m₂² $\int_{0.1}^{0.15}$ dx]

Now, the velocity is given as:

V = √(T/μ)

Now, the kinetic energy becomes,

K = 1/2 T [m₁² (0.1) + m₂² (0.5)]

On substituting the values, we get,

K = 1/2 (10) [(10⁻⁴)² (0.1) + (4 × 10⁻⁴)² (0.5)]

K = 10/2 [10⁻⁴](0.3)

∴ K = 0.15 mJ