Question

If the string is 7.6 m long, has a mass of 34 g , and is pulled taut with a tension of 15 N, how much time does it take for a wave to travel from one end of the string to the other

Answer 1

Answer:

The wave takes 0.132 seconds to travel from one end of the string to the other.

Explanation:

The velocity of a transversal wave ($v$) travelling through a string pulled on both ends is determined by this formula:

$v = \sqrt{\frac{T\cdot L}{m} }$

Where:

$T$ - Tension, measured in newtons.

$L$ - Length of the string, measured in meters.

$m$ - Mass of the string, measured in meters.

Given that $T = 15\,N$, $L = 7.6\,m$ and $m = 0.034\,kg$, the velocity of the tranversal wave is:

$v = \sqrt{\frac{(15\,N)\cdot (7.6\,m)}{0.034\,kg} }$

$v\approx 57.522\,\frac{m}{s}$

Since speed of transversal waves through material are constant, the time required ($\Delta t$) to travel from one end of the string to the other is described by the following kinematic equation:

$\Delta t = \frac{L}{v}$

If $L = 7.6\,m$ and $v\approx 57.522\,\frac{m}{s}$, then:

$\Delta t = \frac{7.6\,m}{57.522\,\frac{m}{s} }$

$\Delta t = 0.132\,s$

The wave takes 0.132 seconds to travel from one end of the string to the other.