Transverse waves travel at $43.2 \mathrm {~m} / \mathrm { s }$ in a string that is subjected to a tension of $60.5 \mathrm {~N}$ If the string is $15.9 \mathrm {~m}$ long, what is its mass?
A) 0.515 kg
B) 0.216 kg
C) 0.366 kg
D) 0.597 kg

Question

Quizplus · Accepted Answer

The correct answer is A.The mass of the string can be calculated using the formula:$$m = \frac{\mu L}{v^2}$$where:* m is the mass of the string in kilograms* \mu is the linear density of the string in kilograms per meter* L is the length of the string in meters* v is the speed of the wave in meters per secondIn this problem, we are given the following information:* v = 43.2 m/s* L = 15.9 m* T = 60.5 NWe can calculate the linear density of the string using the formula:$$\mu = \frac{T}{gL}$$where:* T is the tension in the string in newtons* g is the acceleration due to gravity in meters per second squaredIn this problem, we are given the following information:* T = 60.5 N* g = 9.81 m/s^2* L = 15.9 mSubstituting these values into the formula, we get:$$\mu = \frac{60.5 \mathrm{~N}}{9.81 \mathrm{~m/s^2} 	imes 15.9 \mathrm{~m}} = 0.0366 \mathrm{~kg/m}$$Now we can substitute the values of \mu, L, and v into the formula for the mass of the string:$$m = \frac{0.0366 \mathrm{~kg/m} 	imes 15.9 \mathrm{~m}}{(43.2 \mathrm{~m/s})^2} = 0.515 \mathrm{~kg}$$Therefore, the mass of the string is 0.515 kg.

Transverse Waves Travel At 43.2 m/s43.2 \mathrm {~m} / \mathrm { s }43.2 m/s

Transverse Waves Travel At $43.2 \mathrm {~m} / \mathrm { s }$