Question

A wave is described by y= (2.00cm) sin (kx-wt), where k=2.11rad/m, w=3.62rad/s, x is in meters, t is in seconds. What is the amplitude, wavelength, frequency, and speed of the wave?

Answer 1

In the given wave equation, y = (2.00 cm) sin(kx - wt), we can identify the following parameters:

Amplitude (A) = 2.00 cm Wave number (k) = 2.11 rad/m Angular frequency (ω) = 3.62 rad/s

To determine the wavelength, frequency, and speed of the wave, we need to relate these parameters.

The wave equation can be rewritten as y = A sin(kx - ωt). Comparing this equation with the general form of a sinusoidal wave, y = A sin(kx - ωt), we can observe the following relationships:

Wavelength (λ) = 2π/k Frequency (f) = ω/2π Wave speed (v) = ω/k

Let's calculate these values:

1. Wavelength (λ) = 2π/k λ = 2π/2.11 rad/m λ ≈ 2.99 m

2. Frequency (f) = ω/2π f = 3.62 rad/s / 2π f ≈ 0.577 Hz

3. Wave speed (v) = ω/k v = 3.62 rad/s / 2.11 rad/m v ≈ 1.72 m/s

Therefore, the amplitude of the wave is 2.00 cm, the wavelength is approximately 2.99 m, the frequency is approximately 0.577 Hz, and the speed of the wave is approximately 1.72 m/s.