The wave function of a standing wave is y(x, t) = 4.44 mm sin[(32.5 rad/m)x] sin[(754 rad/s)t]. For the two traveling waves that make up this standing wave, find the (a) amplitude.
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1
Identify the general form of the standing wave equation, which is given by y(x, t) = 2A \sin(kx) \sin(\omega t), where A is the amplitude of the traveling waves, k is the wave number, and \omega is the angular frequency.
Compare the given wave function y(x, t) = 4.44 \text{ mm} \sin[(32.5 \text{ rad/m})x] \sin[(754 \text{ rad/s})t] with the general form to identify the corresponding components.
Notice that the coefficient 4.44 mm in the given equation corresponds to 2A in the general form of the standing wave equation.
Solve for A by dividing the coefficient 4.44 mm by 2, as A = \frac{4.44 \text{ mm}}{2}.
The amplitude A of each of the traveling waves that make up the standing wave is the value obtained from the calculation in the previous step.