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?

Question

Quizplus · Accepted Answer

The correct answer is A because the mass of the string can be calculated using the formula:$$m = \frac{\mu L}{v^2}$$where m is the mass, \mu is the linear density, L is the length of the string, and v is the wave speed. The linear density is given by:$$\mu = \frac{T}{	ext{g}}$$where T is the tension and g is the acceleration due to gravity. Substituting these expressions into the first equation, we get:$$m = \frac{TL}{v^2	ext{g}}$$Plugging in the given values, we get:$$m = \frac{(60.5 \mathrm{~N})(15.9 \mathrm{~m})}{(43.2 \mathrm{~m/s})^2(9.81 \mathrm{~m/s^2})} = 0.515 \mathrm{~kg}$$

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

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