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(D) The equation of a stationary wave is given by $y = A_{res} \sin \omega t$,where $A_{res}$ is the amplitude of the particle at position $x$.Compari

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$5$

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(D) The equation of a stationary wave is given by $y = A_{res} \sin \omega t$,where $A_{res}$ is the amplitude of the particle at position $x$.Comparing the given equation $y = (10 \cos \pi x) \sin \frac{2 \pi t}{T}$ with the standard form,the amplitude at any position $x$ is $A(x) = |10 \cos \pi x|$.Given $x = \frac{4}{3} \, cm$,we substitute this value into the expression:$A = |10 \cos(\pi \cdot \frac{4}{3})|$$A = |10 \cos(\frac{4 \pi}{3})|$Since $\cos(\frac{4 \pi}{3}) = \cos(\pi + \frac{\pi}{3}) = -\cos(\frac{\pi}{3}) = -\frac{1}{2}$,$A = |10 \cdot (-0.5)| = |-5| = 5 \, cm$.Thus,the amplitude is $5 \, cm$.

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