Question

The linear density of a string is 1.9 × 10-4 kg/m. A transverse wave on the string is described by the equation y = (0.034 m) sin[(2.8 m-1)x + (38 s-1)t] What are (a) the wave speed and (b) the tension in the string?

Answer 1

Answer:

a. v = 13.572 m / s

b. T = 2.578 x 10 ⁻³ N

Explanation:

μ = 1.9 x 10 ⁻⁴ kg / m

y = y ₙ * sin ( kx + wt )

a.

y = 0.034 m * sin ( 2.8 m⁻¹) x + (38 s⁻¹)t

R = 2.8 m⁻¹

W = 38 s⁻¹

To determine speed of the string

v = W / R = 38 / 2.8

v = 13.572 m / s

b.

v = √ T / μ

v ² = T / μ

To determine the tension on the string

T = v ² * μ

T = 13.572 m/s * 1.9 x 10 ⁻⁴ kg / m

T = 2.578 x 10 ⁻³ N