A sinusoidal wave traveling on a string is moving in the positive x-direction. The wave has a wavelength of 8 m, a frequency of 60 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 think the function follows this format:
y(x,t)=A*sin(kx-wt+phase shift), but im not sure how apply it to this problem. Any help or suggestions is appreciated, thank you!
Look at the first link in Ralated questions.
thank you very much!
You're on the right track! The wave function you mentioned, y(x,t) = A*sin(kx - wt + phase shift), is a general form that represents a sinusoidal wave. Let's apply it to this specific problem.
In the given problem, we are told that the wave has a wavelength of 8 m, a frequency of 60 Hz, and an amplitude of 9 cm. We can use these values to determine the necessary parameters in the wave function.
The wave equation relates the speed of the wave (v) to its frequency (f) and wavelength (λ) as v = fλ. Rearranging this equation, we can solve for the wave speed: v = 60 Hz * 8 m = 480 m/s.
Now let's look at the wave function: y(x,t) = A*sin(kx - wt + phase shift).
A represents the amplitude, which is given as 9 cm. We need to convert it to meters: A = 9 cm * (1 m / 100 cm) = 0.09 m.
k represents the wave number, which is related to the wavelength by the equation k = (2π) / λ. Plugging in the wavelength of 8 m, we can calculate: k = (2π) / 8 m ≈ 0.7854 rad/m.
w represents the angular frequency, which is related to the frequency by the equation w = 2πf. Plugging in the frequency of 60 Hz, we get: w = 2π * 60 Hz ≈ 376.99 rad/s.
As for the phase shift, there is no information given in this problem, so let's assume it's zero for simplicity.
Putting it all together, the wave function for this particular wave traveling in the positive x-direction can be written as:
y(x,t) = 0.09*sin(0.7854x - 376.99t).
Notice that I used lower case "w" to represent the angular frequency to avoid any confusion with the width "w" in the wave function.