A transverse wave travels on a string of length 1.3 m and diameter 1.1 mm, whose mass is 10 g and which is under a tension of 16 N.What is the linear mass density of the string? A)7.7 x 10^-3 kg/m B)0.13 kg/m C)7.7 kg/m D)46 kg/m E)130 kg/m

Question

Quizplus · Accepted Answer

The linear mass density of the string, denoted by μ, is given by:

μ = m/L

where m is the mass of the string and L is its length.

In this case, m = 10 g = 0.01 kg and L = 1.3 m.

To find the diameter of the string in meters, we need to divide the given diameter of 1.1 mm by 1000 to convert it to meters:

d = 1.1 mm / 1000 = 0.0011 m

The cross-sectional area of the string is A = (π/4)d^2 = (π/4)(0.0011 m)^2 = 9.50 x 10^-7 m^2.

The tension in the string, denoted by F, is related to the wave speed, denoted by v, and the linear mass density by:

v = √(F/μ)

Solving for μ, we get:

μ = F/v^2

The wave speed on the string can be expressed in terms of its tension and linear mass density as:

v = √(F/μ) = √(F L/m)

Substituting the given values, we get:

v = √(16 N x 1.3 m / 0.01 kg) = 16.12 m/s

Substituting this value of v into the previous equation, we get:

μ = 16 N / (16.12 m/s)^2 = 7.7 x 10^-4 kg/m

Therefore, the linear mass density of the string is 7.7 x 10^-4 kg/m, which is closest to answer choice A.

A Transverse Wave Travels on a String of Length 1