A long string carries a wave; a 7.00-m segment of the string contains five complete wavelengths and has a mass of 180 g. The string vibrates sinusoidally with a frequency of 55.0 Hz and a peak-to-valley displacement of 20.0 cm. (The "peak-to-valley" distance is the vertical distance from the farthest positive position to the farthest negative position.)(a) Write the function that describes this wave traveling in the positive x direction. (Use the following as necessary: x and t. x is in meters and t is in seconds.)y =

y = 0.1sin(4.5x - 345.6t)

Explanation:

Parameters given:

Length of 5 wavelengths = 7 m

Length of one wavelength, λ = 7/5 = 1.4 m

Frequency of wave, f = 55 Hz

Peak to Valley displacement = 20 cm = 0.2 m

Amplitude is half of the Peak to Valley displacement = 0.1 m

The wave function of a wave traveling in the positive x direction is given generally as:

y = Asin(kx - wt)

Where A = amplitude

k = Wave factor = 2π/λ

x = displacement on the x axis

w = angular frequency = 2πf

t = time taken

=> Wave factor, k = 2π/λ = 2π/(1.4) = 4.5 m^(-1)

=> Angular frequency, w = 2πf = 2π * 55 = 345.6 Hz

Therefore, inserting all the necessary parameters, we get that the wave function is:

y = 0.1sin(4.5x - 345.6t)

think about the oscillation of the toy shown in the video. when the toy is at the highest point of its motion, its velocity is zero and its acceleration is negative.