For a wave traveling in a string,by what factor would the tension need to be increased to double the wave speed?
A)1.4
B)2.0
C)4.0
D)16

Question

Quizplus · Accepted Answer

The wave speed in a string is given by v = √(T/μ), where T is the tension in the string and μ is the linear density of the string. If the wave speed is doubled, then v' = 2v, and we can write:

2v = √(T'/μ)

where T' is the increased tension needed to achieve this speed. Solving for T', we get:

T' = 4T

Therefore, the tension must be increased by a factor of 4 to double the wave speed. The closest answer choice is C, 4.0.

For a Wave Traveling in a String,by What Factor Would