Question

The wave speed on a string is 150 m/s when the tension is 75 N. What tension will give a speed of 180 m/s?

Short answer

The tension of the string is 108 N

Step-by-step solution

Step 1. Write the given information

The speed of the wave is given by v₁= 150m/s

The tension of the string is T₂=75N

The tension of the string is changed

The new speed of the string is v₂= 180m/sec

Step 2. To determine the new tension of the string

The formula for the speed of the wave is given by

$v=\sqrt{\frac{T}{\mu }}$

Here µ is the effective mass of the string

As it can be observed that the speed is directly proportional to the square root of tension of the string

$v\mathit{\propto }\sqrt{\mathit{T}}$

The new tension is given by
$\frac{v_1}{v_2}=\frac{\sqrt{T_1}}{\sqrt{T_2}}$
substitute the values,

localid="1649317557949" role="math" $$\begin{gathered} \frac{150m/s}{180m/s}=\frac{\sqrt{75N}}{\sqrt{T_2}} \\ {\left(\frac{150}{180}\right)}^2=\frac{75N}{T_2} \\ {T}_2=\frac{\left(75N\right)(180\times 180)}{150\times 150} \\ {T}_2=108N \end{gathered}$$

Therefore, the tension of the string is 108 N