A string of mass m is under tension, and the speed of a wave in the string is v. What will be the speed of a wave in the string if the mass of the string is increased to 2m but with no change in the length or tension?
A) v/2
B) v/ $\sqrt { 2 }$
C) v $\sqrt { 2 }$
D) 2v
E) 4v

Question

Quizplus · Accepted Answer

The speed of a wave on a string is given by 
v = √(T/μ)
where T is the tension in the string and μ is the linear mass density (mass per unit length) of the string. Since the length and tension of the string are constant, the speed of the wave is directly proportional to the square root of the linear mass density. When the mass of the string is increased to 2m, the linear mass density doubles (μ → 2μ), so the speed of the wave decreases by a factor of √2 (v → v/√2). Therefore, the correct answer is B.

A String of Mass M Is Under Tension, and the Speed