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To find the maximum amplitude, we need to consider when the sine function reaches its maximum value. The sine function reaches its maximum value when the argument, 2πft, is equal to π/2. So we have: 2πft = π/2 Now, let's solve for t: t = (1/4f) Now, we substitute this value of t back into the sine wave equation: A(t) = A₀ * sin(2πf * (1/4f)) Simplify: A(t) = A₀ * sin(π/2) The sine of π/2 is 1, so: A(t) = A₀ * 1 This simplifies to: A(t) = A₀ So, the maximum amplitude of a sine wave is equal to the peak amplitude, which is represented by A₀. - A sine wave can be represented as: A(t) = A₀ * sin(2πf(t)), where A(t) is the amplitude at time t, A₀ is the peak amplitude, f(t) is the frequency at time t. - The derivation involves understanding the behavior of a sine function and how it reaches its maximum value, which is the amplitude.Also Check - Measurement Formula