A string under tension carries a transverse wave traveling at speed v.If the tension in the string is halved,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 under tension is given by v=√(T/μ), where T is the tension in the string and μ is the linear mass density. If the tension in the string is halved, the wave speed becomes v'=√(T'/μ). Since T' = T/2, we have v' = √(T/2μ) = (√2/2) √(T/μ) = (√2/2) v. Therefore, the wave speed decreases to about 71% of v.

A String Under Tension Carries a Transverse Wave Traveling at Speed