The wave speed on a string under tension is 100 m/s. What is the speed if the tension is doubled?

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lemjay | High School Teacher | (Level 3) Senior Educator

Posted on

The speed of a wave on a stretch string is:

`v = sqrt(T/(m/L))`

where v - speed of the wave

         T - string tension

        m - mass of string

         L - length of string

Using the formula above, solve for T when wave speed is 100 m/s.

`v = sqrt(T/(m/L))`

`100 = sqrt [T/(m/L)]`

To remove the radical sign, square both sides.

`100^2 = T/(m/L)`

`100^2 * m/L = T`

Then, solve for v when value of T is doubled.

So, multiply T by 2.

`v = sqrt((2*T)/(m/L))`

Substitute `T=100^2*m/L` .

`v = sqrt ((2*100^*m/L)/(m/L)) = sqrt(2*100^2) = 100sqrt2 ~~ 141.4`

Hence, when T is doubled, the wave speed increases from 100 m/s to 141.4 m/s.



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