Waves on a string: 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.

Question

Quizplus · Accepted Answer

The maximum transverse acceleration $a_{max}$ of a point on the wire can be calculated using the formula for the acceleration of a simple harmonic oscillator, $a_{max} = -\omega^2 A$, where $\omega$ is the angular frequency and $A$ is the amplitude. The angular frequency $\omega$ can be found from the frequency $f$ using the relation $\omega = 2\pi f$. Given $f = 570 \, \text{Hz}$ and $A = 3.7 \, \text{mm} = 0.0037 \, \text{m}$, we calculate $\omega = 2\pi(570) \approx 3580 \, \text{rad/s}$. Thus, $a_{max} = -(3580)^2(0.0037) \approx -47,000 \, \text{m/s}^2$.

Waves on a String: a 8