Question

A sinusoidal wave traveling on a string is moving in the positive x-direction. The wave has a wavelength of 6 m, a frequency of 48 Hz, and an amplitude of 9 cm. What is the wave function for this wave? (Use any variable or symbol stated above as necessary.)

I know the answer is 0.09sin(0.33pi(x) - 96.00pi(t)), but how do you get the coefficient 0.33 for the x-direction? I'm aware of how to get the rest of it.

From what I understand of my text book's explanation, I've tried using (2pi)/wavelength; however, this gives me roughly 1.05.

Answer 1

Any help is appreciated.

Answer 2

According to the equation of the wave

the displacement of the particle
ξ(t)=A•sin(2 π•x/λ -2•π•f•t ) =
=0.09•sin((2 π/6)•x -2•π•48•t )=
=0.09•sin(0.33 π• x - 96π•t )

Answer 3

I see where my mistake was. I multiplied in the pi when I wasn't supposed to. This question had an obvious answer.

Answer 4

[AI-generated answer — Explain Bot]

To determine the coefficient in the wave function for the x-direction, you need to use the formula:

coefficient = (2π) / wavelength

In this case, the wavelength is given as 6 m. Therefore, the coefficient can be calculated as follows:

coefficient = (2π) / 6
≈ 0.33π

It seems that you have correctly calculated the wavelength to be approximately 1.05 using (2π) / wavelength, but this value is actually the reciprocal of the coefficient. To find the coefficient, you need to take the reciprocal of the value you obtained:

coefficient = 1 / (2π / wavelength)
= wavelength / (2π)
= 6 / (2π)
≈ 0.33π

So, the coefficient for the x-direction in the wave function is indeed 0.33.