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