A sinusoidal wave travels along a stretched string.A point along the string has a maximum velocity of 1 m/s and a maximum displacement of 2 cm.What is the maximum acceleration at that point? A)10 m/s² B)50 m/s² C)30 m/s² D)15 m/s² E)20 m/s²

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Quizplus · Accepted Answer

The maximum acceleration $a_{max}$ in a sinusoidal wave is given by $a_{max} = \omega^2 \times A$, where $\omega$ is the angular frequency and $A$ is the maximum displacement. The angular frequency $\omega$ can be found from the maximum velocity $v_{max} = \omega \times A$. Given $v_{max} = 1$ m/s and $A = 2$ cm = 0.02 m, we find $\omega = \frac{v_{max}}{A} = \frac{1}{0.02} = 50$ rad/s. Therefore, $a_{max} = \omega^2 \times A = 50^2 \times 0.02 = 50$ m/s$^2$.

A Sinusoidal Wave Travels Along a Stretched String