Question

A transverse wave propagating along the string is y = 0.3 sin (x + 20t) where x, y are in metre and t in second. The linear density of the string is 1.2 x 10^-4 kg/m. The tension in the string is ______.

Options

• 0.072 N

• 0.024 N

• 0.096 N

• 0.048 N

Answer 1

A transverse wave propagating along the string is y = 0.3 sin (x + 20t) where x, y are in metre and t in second. The linear density of the string is 1.2 x 10^-4 kg/m. The tension in the string is 0.048 N.

Explanation:

y = 0.3 sin (x + 20t)

v = `sqrt("T"/"m")`   ∴ T = v²m

`"dy"/"dt" = 0.3 xx 20 cos (x + 20"t")`

`("dy"/"dt")_"max" = 6`

∴ T = 3.6 × 1.2 × 10^-4 kg/m

= 43.2 × 10^-4 kg

= 0.00432 = 0.0423 N