Question

For a sine function with amplitude =0.75 and period =10 , what is y(4) ?

Answer 1

To find the height of a sine wave at a specific position and time, use the formula y(x, t) = A sin(kx - wt + φ), where A is the amplitude, k is the wave number, w is the angular frequency, and φ is the initial phase shift.

Step-by-step explanation:

To find the height of the wave at position x = 3.00 m and time t = 10.0 s, we can use the formula for a sine function: y(x, t) = A sin(kx - wt + φ), where A is the amplitude, k is the wave number, w is the angular frequency, and φ is the initial phase shift.

In this case, the amplitude A is 0.75 and the period T is 10. Since period T is the reciprocal of the angular frequency w, we can use the formula w = 2π/T to find w. Plugging in T = 10, we get w = 2π/10 = π/5.

Now we can substitute the values into the formula and solve for y(3.00, 10.0): y(3.00, 10.0) = 0.75 sin(k(3.00) - (π/5)(10.0) + φ).

Answer 2

The general formula for sine function is y(x) = A sin(2πx/t). Here, x = displacement = 4 , time period , t = 10 and Amplitude, A = 0.75, then, y(4) = 0.75 sin( 2π*4/10) = 0.75*0.04 =0.03. Thus, the value of y(4) wll be 0.03