Question

In this experiment, you will plot a graph: frequency vs number of anti-nodes. Write an equation that shows how the wave velocity relates to the slope of this graph and the length of the string. (Use the following as necessary: v for wave velocity and L for the length of the string.)

Answer 1

The equation that shows how wave velocity relates to the slope of a frequency vs number of anti-nodes graph and the length of the string is v = 2Lm, where 'm' is the slope and 'L' is the length of the string.

Step-by-step explanation:

The equation you are looking for that relates the wave velocity to the slope of the graph and the length of the string is derived from the general wave equation v = fλ (velocity equals frequency times wavelength). Since you're plotting frequency vs number of anti-nodes, the number of anti-nodes (n) is equal to one-half the number of wavelengths (λ) in a standing wave for a string of length (L), as L = nλ/2. Therefore, the frequency (f) can be represented as f = nv/(2L). Taking the slope (m) of the graph frequency vs number of anti-nodes, where the slope is calculated as rise over run (Δf/Δn), we relate it back to the velocity and length of the string using the equation v = 2Lm, where 'm' is the slope of the graph.