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/ sq. rt. of 2

B) v/2

C) 2v

D) v * sq. rt. of 2

E) 4v

Answer:A) v/ sq. rt. of 2

Explanation:The speed of the wave in the string is defined as:

[tex]v=\sqrt{\frac{T}{\mu}}[/tex]

Where T is the tension on the string and [tex]\mu[/tex] is the linear density, that is, the mass per unit length:

[tex]\mu=\frac{m}{L}[/tex]

Where m is the mass of the string and L its length. We have [tex]m’=2m[/tex], [tex]T’=T[/tex] and [tex]L’=L[/tex]:

[tex]v’=\sqrt\frac{T’}{m’/L’}\\v’=\sqrt\frac{T}{2m/L}\\v’=\frac{1}{\sqrt2}\sqrt\frac{T}{m/L}\\v’=\frac{v}{\sqrt2}[/tex]

Explanation:

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