A string under tension carries a transverse wave traveling at speed v.If the tension in the string is halved and the linear density of the string is quadrupled,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 = sqrt(T/μ)

where T is the tension in the string and μ is its linear mass density.

If the tension is halved and the linear density is quadrupled, we have:

T' = T/2
μ' = 4μ

Using the above equation, the new wave speed is:

v' = sqrt(T'/μ') = sqrt[(T/2)/(4μ)] = sqrt(T/32μ)

Therefore, the wave speed decreases to about 71% of v. So, the correct choice is D.

A String Under Tension Carries a Transverse Wave Traveling at Speed