A string is stretched with a tension of 100 N. The string has a length of 2.00 meters. The velocity of wave propagation along the string is 220 m/s. The mass of the string is
A) 3.75 g.
B) 4.13 g.
C) 4.66 g.
D) 5.21 g.
E) 5.74 g.

Question

Quizplus · Accepted Answer

The wave speed can be related to the tension, mass per unit length, and length of the string via the equation:

v = sqrt(T/(m/L))

where v is the wave speed, T is the tension, m/L is the mass per unit length, and sqrt() denotes taking the square root. Solving for m/L, we get:

m/L = T/v^2

Substituting in the given values, we have:

m/L = 100/220^2 = 0.00206 kg/m

Multiplying by the length of the string, we get the total mass:

m = m/L * L = 0.00206 kg/m * 2.00 m = 0.00412 kg

Converting to grams, we get:

m = 4.12 g

The closest answer choice is B) 4.13 g, so that is the best choice.

A String Is Stretched with a Tension of 100 N