A 8.0-m long wire with a mass of 10 g is under tension. A transverse wave for which the frequency is 570 Hz, the wavelength is 0.10 m, and the amplitude is 3.7 mm is propagating on the wire. The maximum transverse acceleration of a point on a wire is closest to A) 47,000 m/s². B) 41,000 m/s². C) 35,000 m/s². D) 29,000 m/s². E) 53,000 m/s².

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Quizplus · Accepted Answer

The maximum transverse acceleration of a point on a wire is given by:$$a_{max} = \omega^2 A$$where $\omega$ is the angular frequency and $A$ is the amplitude.The angular frequency is given by:$$\omega = 2\pi f$$where $f$ is the frequency.Substituting the given values into these equations, we get:$$\omega = 2\pi (570 ext{ Hz}) = 3570 ext{ rad/s}$$$$a_{max} = (3570 ext{ rad/s})^2 (0.0037 ext{ m}) = 47,000 ext{ m/s}^2$$Therefore, the maximum transverse acceleration of a point on the wire is closest to 47,000 m/s².

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