Questions: 2. A 0.65 meter long string is stretched to a tension of 3.75 N . A wave with a frequency of 185 Hz and a wavelength of 0.44 m travels on the string. What is the mass of the string?

Solution Steps

The wave speed $v$ on the string can be calculated using the relationship between frequency $f$ and wavelength $\lambda$: $$v = f \lambda$$ Given: $$f = 185 \, \text{Hz}, \quad \lambda = 0.44 \, \text{m}$$ $$v = 185 \times 0.44 = 81.40 \, \text{m/s}$$

The wave speed on a string is also related to the tension $T$ and the linear mass density $\mu$ by the equation: $$v = \sqrt{\frac{T}{\mu}}$$ Rearranging to solve for $\mu$: $$\mu = \frac{T}{v^2}$$ Given: $$T = 3.75 \, \text{N}, \quad v = 81.40 \, \text{m/s}$$ $$\mu = \frac{3.75}{(81.40)^2} = \frac{3.75}{6622.76} \approx 0.0005661 \, \text{kg/m}$$

The mass $m$ of the string can be found by multiplying the linear mass density $\mu$ by the length $L$ of the string: $$m = \mu L$$ Given: $$L = 0.65 \, \text{m}$$ $$m = 0.0005661 \times 0.65 \approx 0.0003670 \, \text{kg}$$

Final Answer