Two strings are made of the same material. String 1 has radius r₁ while string 2 has radius r₂ = r₁/2. When stretched by the same tension, the respective speed of propagation of waves v₁ and v₂ satisfy the condition A) v₁ = v₂. B) v₁ = 2v₂. C) v₁ = v₂/ . D) v₁ = v₂/2. E) v₁ = v₂/4.

Question

Quizplus · Accepted Answer

The speed of propagation of waves in a string is given by v = sqrt(T/μ), where T is the tension and μ is the linear mass density (mass per unit length) of the string. The linear mass density of a string is proportional to the square of its radius, so μ₂ = (1/4)μ₁. Therefore, the speed of propagation of waves in string 2 is v₂ = sqrt(T/((1/4)μ₁)) = 2sqrt(T/μ₁) = 2v₁. Therefore, the correct choice is D: v₁ = v₂/2.

Two Strings Are Made of the Same Material