Final answer:
The frequency of the wave can be found by dividing the angular frequency by 2π, the wavelength by dividing 2π by the wavenumber, and the speed by multiplying the frequency and wavelength.
Step-by-step explanation:
The displacement of a wave is given by the function D(y,t) = (5.90 cm) sin(6.30y + 62.0t), where y is in meters and t is in seconds. To find the frequency, wavelength, and speed of the wave, we can analyze this wave equation.
a) Frequency of the wave
The angular frequency \( \omega \) is the coefficient of t in the wave equation, which is 62.0 s−1. The actual frequency f can be found using the relation f = \( \omega / 2\pi \). Therefore, the frequency of the wave is f = 62.0 / (2\pi) Hz.
b) Wavelength of the wave
The wavenumber k is the coefficient of y in the wave equation, which is 6.30 m−1. The wavelength \( \lambda \) can be calculated using the relation \( \lambda = 2\pi / k \). Thus, the wavelength is \( \lambda = 2\pi / 6.30 m.
c) Speed of the wave
The speed v of the wave can be found using the relation v = f \( \lambda \). After finding the frequency and wavelength, we can calculate the speed of the wave.