A wave traveling in the +x direction has an amplitude of 0.50 m, a speed of 5.7 m/s, and a frequency of 18 Hz. Write the equation of the wave in the form given by either Equation 16.3 or 16.4. (Answer in terms of t and x. Assume standard units.)
please check my answer:
y= A sin (2pift-2pi(x)/wavelength (formula)
y=.5msin[2pi*18hz)t-(2pi)x/.31667]
correct.
Your answer is partially correct. The equation you provided is almost in the correct form, but there is a mistake in the denominator of the denominator. Instead of dividing by the wavelength, you should divide by the wave number (k). The wave number (k) is equal to 2π divided by the wavelength (λ).
So, the correct equation of the wave in the given form is:
y = A sin(2πft - 2πx/λ)
Substituting the values:
A = 0.50 m
f = 18 Hz
v = 5.7 m/s
We can calculate the wavelength (λ) using the formula:
v = fλ
λ = v / f
λ = 5.7 m/s / 18 Hz
λ ≈ 0.31667 m
Now, substituting the values of A, f, and λ, the correct equation of the wave becomes:
y = 0.50 m sin(2π * 18 Hz * t - (2π/0.31667 m) * x)
So, the correct equation of the wave is:
y = 0.50 m sin(36πt - 19.881x)