Question

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

Answer 1

The amplitude of the wave is 0.30 m. The wavelength is 1.47 m. The frequency is 0.577 Hz. The speed of the wave is 0.849 m/s.

Step-by-step explanation:

The given wave equation is y(x, t) = (0.30 m)sin [4.30m π (x - 18.00mt)].

The amplitude of the wave is 0.30 m.

The wavelength can be determined using the formula λ = 2π/k, where k is the wave number. In this case, λ = 2π/4.30 m⁻¹ = 1.47 m.

The frequency can be calculated using the formula f = w/2π, where w is the angular frequency. Thus, f = 3.62 rad/s / 2π = 0.577 Hz.

The speed of the wave can be found by multiplying the wavelength and frequency: v = λ * f = 1.47 m * 0.577 Hz = 0.849 m/s.

Answer 2

The amplitude of the wave is 2.00 cm.

The speed of the wave is 1.72 m/s.

The frequency of the wave is 0.58 Hz.

The wavelength of the wave is 2.97 m.

How to calculate the amplitude, frequency, speed of the wave?

The amplitude, wavelength, frequency, and speed of the wave is calculated as follows;

y = 2.00 cm) sin(kx – ωt)

where;

• k = 2.11 rad/m
• ω = 3.62 rad/s

The amplitude of the wave = 2.00 cm

The speed of the wave is calculated as;

v = ω / k

where;

• ω is the angular speed
• k is the wave number

v = (3.62 ) / 2.11

v = 1.72 m/s

The frequency of the wave is calculated as follows;

ω = 2πf

f = ω / 2π

f = (3.62 ) / 2π

f = 0.58 Hz

The wavelength of the wave is calculated as;

λ = v / f

λ = (1.72 m/s ) / (0.58 Hz)

λ = 2.97 m