If the tension in a guitar string is increased fourfold without changing its mass or length, how will the speed of the wave on the string change?Select one:a.It will remain the sameb.It will quadruplec.It will halved.It will double
Question
If the tension in a guitar string is increased fourfold without changing its mass or length, how will the speed of the wave on the string change?Select one:a.It will remain the sameb.It will quadruplec.It will halved.It will double
Solution
The speed of a wave on a string is given by the formula v = sqrt(T/μ), where T is the tension in the string and μ is the linear mass density (mass/length).
If the tension in the string is increased fourfold (i.e., T becomes 4T), the speed of the wave becomes v' = sqrt(4T/μ) = 2sqrt(T/μ) = 2v.
So, the speed of the wave on the string will double.
Therefore, the correct answer is d. It will double.
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