Question

A sinusoidal wave traveling in the negative x direction (to the left) has an amplitude of 20.0 cm , a wavelength of 35.0 cm , and a frequency of 12.0Hz . The transverse position of an element of the medium at t = 0, x = 0 is y = -3.00 cm , and the element has a positive velocity here. We wish to find an expression for the wave function describing this wave.(d) the angular frequency ω and

Answer 1

The expression for the wave function describing this wave is y(x,t) = 0.02 sin(17.95x + 75.4t - 0.00198).

The angular frequency of a wave  is 75.4 rad/s.

What is wave function?

A wave function is a mathematical equation for the motion of the wave.

y(x, t) = A sin(kx + ωt + Φ)

where;

• ω is angular speed
• k is angular wavenumber
• Φ is phase angle

The angular wave number of the wave is calculated as follows;

k = 2π/λ

where;

• λ is the wavelength
• k is the angular wavenumber

k = 2π / 0.35

k = 17.95/m

Angular speed

ω = 2πf

ω = 2π(12)

ω = 75.4 rad/s

Phase angle

75.4(0.2) sin(Φ) = -0.03

sin(Φ) = -0.001989

Φ = arc sin(-0.001989)

Φ = -0.00198

Wave function

y(x,t) = 0.02 sin(17.95x + 75.4t - 0.00198)

Thus, the expression for the wave function describing this wave is y(x,t) = 0.02 sin(17.95x + 75.4t - 0.00198).

Learn more about wave function here: brainly.com/question/22675050

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