**Problem Statement:**One end of the horizontal rope is attached to a prong of an electrically driven tuning fork that vibrates a rope transversely at 250 Hz. The other end passes over a pulley and supports a 3 kg mass. The linear mass density of the rope is 0.048 kg/m.**Question:**What is the speed of transverse waves on the rope? (m/s)**Solution:**To determine the speed of transverse waves on the rope, we can use the following formula for wave speed on a rope under tension:\[ v = \sqrt{\frac{T}{\mu}} \]where:- \( v \) is the wave speed,- \( T \) is the tension in the rope,- \( \mu \) is the linear mass density of the rope.**Step-by-step Calculation:**1. **Calculate the tension in the rope (T):** Tension (T) is created by the weight of the mass hanging at the end of the rope. \[ T = mg \] where: - \( m \) is the mass (3 kg), - \( g \) is the acceleration due to gravity (approximated as 9.8 m/s²). Substitute the values: \[ T = 3 \, \text{kg} \times 9.8 \, \text{m/s}^2 \] \[ T = 29.4 \, \text{N} \]2. **Calculate the wave speed (v):** Use the formula for the wave speed: \[ v = \sqrt{\frac{T}{\mu}} \] where: - \( \mu \) is given as 0.048 kg/m. Substitute the values: \[ v = \sqrt{\frac{29.4 \, \text{N}}{0.048 \, \text{kg/m}}} \] \[ v = \sqrt{612.5 \, \text{m}^2/\text{s}^2} \] \[ v \approx 24.74 \, \text{m/s} \]**Answer:**The speed of transverse waves on the rope is approximately 24.74 m/s.

One end of the horizontal rope is attached to a prong of an electrically driven tuning fork that vibrates a rope transversely at 250HZ. The other end passes over a pulley and supports at 3 kg mass. The liner mass density of the rope is 0.048 kg/m. What is the speed of a transverse waves on the rope? (m/s)

One end of the horizontal rope is attached to a prong of an electrically driven tuning fork that vibrates a rope transversely at 250HZ. The other end passes over a pulley and supports at 3 kg mass. The liner mass density of the rope is 0.048 kg/m. What is the speed of a transverse waves on the rope? (m/s)

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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