A string wave equation is given by y=0.002 cos (300 t-15 x) and mass density is μ=0.1 kg / m. Then find the tension force in the string.

Question

A string wave equation is given by y=0.002 cos (300 t-15 x) and mass density is μ=0.1 kg / m. Then find the tension force in the string. (A) 30 N (B) 20 N (C) 40 N (D) 45 N

Tardigrade Admin · Accepted Answer

Given, wave equation, y=0.002 cos (300 t-15 x) Mass density, μ=0.1 kg / m Comparing the given wave equation with y=a cos (ω t-k x), we have ω=300 rad s -1, k=15 rad m -1 ∴ Velocity of wave, v=(ω/k)=(300/15)=20 m / s Wave speed in string is also given by v=√(T/μ) where, T= tension in the string and μ= mass per unit length of string. Substituting the values in Eq. (i), we get 20 =√(T/0.1) ⇒ 400=(T/0.1) ⇒ T =40 N

Q. A string wave equation is given by $y = 0.002 cos (300 t - 15 x)$ and mass density is $μ = 0.1 k g / m$ . Then find the tension force in the string.

$30 N$

$20 N$

$40 N$

$45 N$

Q. A string wave equation is given by y=0.002cos(300t−15x) and mass density is μ=0.1kg/m. Then find the tension force in the string.

30N

20N

40N

45N

Q. A string wave equation is given by $y = 0.002 cos (300 t - 15 x)$ and mass density is $μ = 0.1 k g / m$ . Then find the tension force in the string.

$30 N$

$20 N$

$40 N$

$45 N$