Question

A transverse wave is propagating on the string. The linear density of a vibrating string is 10^-3 kg/m. The equation of the wave is Y = 0.05 sin (x + 15 t) where x and Y are measured in metre and time in second. The tension force in the string is ______,

Options

• 0.2 N

• 0.250 N

• 0.225 N

• 0.325 N

Answer 1

A transverse wave is propagating on the string. The linear density of a vibrating string is 10^-3 kg/m. The equation of the wave is Y = 0.05 sin (x + 15 t) where x and Y are measured in metre and time in second. The tension force in the string is 0.225 N.

Explanation:

Given that, the linear mass density,

m = 10^-3 kg/m and equation of the wave

y = 0.05 sin (x + 15t)    ...(i)

Since, the general equation of wave,

y = a sin(kx + ωt) ... (ii)

Now, comparing the Eqs. (i) and (ii) we get,

k = 1, λ = 2π    ...`(because "k" = (2pi)/lambda)`

and ω = 15 ⇒ f = `15/(2pi)`   ...(∵ ω = 2πf)

Velocity of the wave, v = fλ = `2pi xx 15/(2pi)` = 15 m/s

As, we know, the tension force in the string,

T = v²m     ....`(because "v" = sqrt("T"/"m"))`

So, by substituting the values in the above relation, we get

T = (15)² × 10^-3 = 0.225 N

Hence, the tension force in the string is 0.225 N.