A string with a length of 1.20 m has a mass of 4.00 g. The velocity of wave propagation along the string is 185 m/s. The tension of the stretched string is
A) 162 N.
B) 145 N.
C) 130 N.
D) 114 N.
E) 102 N.

Question

Quizplus · Accepted Answer

The tension in the string can be calculated using the formula for the velocity of a wave on a string: $v = \sqrt{\frac{T}{\mu}}$, where $v$ is the velocity of the wave, $T$ is the tension in the string, and $\mu$ is the mass per unit length of the string. Rearranging the formula to solve for $T$ gives $T = \mu v^2$. The mass per unit length, $\mu$, is the total mass of the string divided by its length, which is $4.00 \, \text{g} / 1.20 \, \text{m} = 3.33 \, \text{g/m} = 0.00333 \, \text{kg/m}$ (converting grams to kilograms). Substituting the given values into the rearranged formula yields $T = 0.00333 \, \text{kg/m} \times (185 \, \text{m/s})^2 = 113.64 \, \text{N}$, which rounds to $114 \, \text{N}$, corresponding to choice D.

A String with a Length of 1