Question

People of the Inca Empire built a long series of roads and rope bridges in the highlands of Peru. Imagine a couple of brave kids playing on such a bridge. By jumping up and down at a frequency of 0.52 Hz, they set up a standing wave with a node on each end and one in the middle. If the bridge is 47.6 m long, what is the speed of the wave? m/s

Answer 1

By calculating the standing wave formed on the rope bridge and given the frequency, the wave speed on the bridge is found to be 33.00 m/s.

Step-by-step explanation:

The problem involves calculating the speed of a wave on a rope bridge when kids create a standing wave with a specific frequency. Given that the frequency of the wave is 0.52 Hz and the length of the bridge is 47.6 m with a node on each end and one in the middle, we can say that this is the second harmonic of the wave since there are two segments (one and a half wavelengths) in the bridge's length.

To find the wavelength (λ), we need to remember that one full wavelength would be twice the length of the bridge because one and a half wavelengths fit into the bridge. So λ = (2 * 47.6 m) / 1.5 = 63.47 m. Now that we have the wavelength, we can find the speed (v) of the wave using the formula v = f * λ, where f is the frequency. Therefore, v = 0.52 Hz * 63.47 m = 33.00 m/s.