Question

Transverse waves travel through a string where the tension equals 13.89 N with a speed of 24.54 m/s. What tension would be required for a wave speed of 28.34 m/s?

Round your answer to 2 decimal places

Answer 1

Express the velocity on terms of tension and mass per unit length:

$$v=\sqrt{\frac T\mu},\\\space\\ \mu=\frac{ T}{v^2}.$$

Since we use the same spring, the mass per unit length is the same, which means that the following tension is required to get another velocity $u$:

$$T_a=\mu u^2=T\frac{u^2}{v^2}=18.52\text{ N}.$$