A string under tension carries a transverse wave traveling at speed v.If the tension in the string is quadrupled and the linear density of the string is doubled,what is the wave speed?
A)The wave speed is unchanged.
B)The wave speed is halved.
C)The wave speed is quadrupled.
D)The wave speed decreases to about 71% of v.
E)The wave speed increases by about 41%.

Question

Quizplus · Accepted Answer

The wave speed in a string is given by $v = \sqrt{\frac{T}{\mu}}$, where $T$ is the tension and $\mu$ is the linear density. If the tension is quadrupled ($T' = 4T$) and the linear density is doubled ($\mu' = 2\mu$), the new speed $v' = \sqrt{\frac{4T}{2\mu}} = \sqrt{2} \cdot \sqrt{\frac{T}{\mu}} = \sqrt{2} \cdot v$. Since $\sqrt{2} \approx 1.41$, the wave speed increases by about 41%.

A String Under Tension Carries a Transverse Wave Traveling at Speed