Question

Use the wave equation to find the speed of a wave given in terms of the general function h(x, t): y(x, t) = (4.20 mm)h[(31 m^ ⁻¹ )x - (6.3 s^ ⁻¹ )t]?

Answer 1

The speed of the wave given by the function y(x, t) = 4.20 mm h[(31 m^ −¹ )x - (6.3 s^ −¹ )t] is 0.20 m/s.

Step-by-step explanation:

To find the speed of a wave given the wave function y(x, t) = 4.20 mm h[(31 m^ −¹ )x - (6.3 s^ −¹ )t], we need to analyze the argument of the function h. The general form of a wave function is y(x, t) = A h(kx − ωt), where A is the amplitude, k is the wave number, and ω is the angular frequency. In the given function, k = 31 m−¹ and ω = 6.3 s−¹.

The wave speed v can be found using the dispersion relation ω = kv, which gives v = ω / k. Substituting the known values, we get v = 6.3 s−¹ / 31 m−¹ = 0.20 m/s.