Question

You take a set of measurements for the wavelengths and frequencies of standing waves on a string that is under a tension of 1.91 N. You use your data to create a plot of wavelength (in m ) vs inverse frequency (in s) and the linear fit of your graph gives a slope of 17.7. What is the linear mass density of the string in kg/m ?

Answer 1

The linear mass density of the string can be calculated from the slope of the wavelength vs inverse frequency graph, which gives the wave speed, and the given tension. Using the formula μ = T/v², the linear mass density is found to be 0.0061 kg/m.

Step-by-step explanation:

To determine the linear mass density (μ) of the string, we can use the relationship between the wave speed (v), wavelength (λ), and frequency (f) of a wave on a string under tension (T): v = λ * f. From the slope of your wavelength (in m) vs inverse frequency (in s) graph, we have the wave speed v since the slope represents λ * (1/f) = v.

The wave speed is also related to the tension and linear mass density by the equation v = √(T/μ). Rearranging this to solve for μ gives us μ = T/v². Now that we have the slope as the wave speed (17.7 m/s) and are given the tension (1.91 N), we can calculate:

μ = 1.91 N / (17.7 m/s)²

= 1.91 N / (313.29 m²/s²)

= 0.0061 kg/m

Thus, the linear mass density of the string is 0.0061 kg/m.