This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Identify the general form of a progressive wave equation and compare it with the given equation. The general equation for a progressive wave moving in the positive x-direction is: y = A ( t - kx) The given wave equation is: y = a (150 t - ( x)/(4)) By comparing these two equations, we can see that the term representing the phase constant due to position x is ( x)/(4). This term represents the phase difference from the origin at a given position x. Step 2: Convert the given phase difference from degrees to radians. The problem states that the phase difference is 45^. To use this in the equation, we must convert it to radians: Phase difference = 45^ × radians180^ Phase difference = ()/(4) radians Step 3: Equate the phase constant from the equation to the given phase difference. The phase constant in the wave equation is ( x)/(4). We are given that this phase difference is ()/(4) radians. ( x)/(4) = ()/(4) Step 4: Solve for x. To solve for x, we can multiply both sides of the equation by 4: x = Then, divide both sides by : x = ()/() x = 1 Step 5: State the units. The options are given in cm, so the value of x is 1 cm. The final answer is D. Last free one today — make it count tomorrow, or type /upgrade for unlimited.