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 $15.9 \text { m }$ 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 speed of a transverse wave on a string is given by the equation:
$$\mathrm v = \sqrt{\frac{\mathrm T}{\mu}},$$
where $\mathrm T$ is the tension in the string and $\mu$ is its linear mass density (mass per unit length).
Rearranging the equation, we get:
$$\mu = \frac{\mathrm T}{\mathrm v^2}.$$
Substituting the given values, we get:
$$\mu = \frac{60.5 \mathrm{~N}}{(43.2 \mathrm{~m/s})^2} \approx 0.515 \mathrm{~kg/m}.$$
The mass of the string is then given by:
$$\mathrm m = \mu \mathrm L = 0.515 \mathrm{~kg/m} \times 15.9 \mathrm{~m} \approx 8.2\mathrm{~kg}.$$
Therefore, the answer is A, 0.515 kg (rounded to three significant figures).

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

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