Question

A wave pulse travels along a stretched string at a speed of 100 cm/s. What will be the speed in cm/s if the string's tension is quadrupled, the length halved and its mass is doubled

Answer 1

Answer:

The new velocity of the string is 100 centimeters per second (1 meter per second).

Explanation:

The speed of a wave through a string ($v$), in meters per second, is defined by the following formula:

$v = \sqrt{\frac{T\cdot L}{m} }$ (1)

Where:

$T$ - Tension, in newtons.

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

$m$ - Mass of the string, in kilograms.

The expression for initial and final speeds of the wave are:

Initial speed

$v_{o} = \sqrt{\frac{T_{o}\cdot L_{o}}{m_{o}} }$ (2)

Final speed

$v = \sqrt{\frac{(4\cdot T_{o})\cdot (0.5\cdot L_{o})}{2\cdot m_{o}} }$

$v = \sqrt{\frac{T_{o}\cdot L_{o}}{m_{o}} }$ (3)

By (2), we conclude that:

$v =v_{o}$

If we know that $v_{o} = 1\,\frac{m}{s}$, then the new speed of the wave in the string is $v = 1\,\frac{m}{s}$.