Ulaby problem 1.10

  • Ulaby
  • Electromagnetics
  • FE Exam
  • PE Exam
  • Wave math

posted on 31 Aug 2016

Ulaby Problem 1.10

Problem Statement

An oscillator that generates a sinusoidal wave on a string completes 20 vibrations in 50 s. The wave peak is observed to travel a distance of 2.8 m along the string in 5 s. What is the wavelength? 1

Analysis and Solution

Frequency is calculated:

\[f = \frac{20}{50 \; m}\]

Propogation velocity is calculated: \(\mu_p = \frac{2.8 \; m}{5 \; s}\)

Spatial wavelength is calculated \(\begin{aligned} \mu_p &= f \lambda \\ \frac{\mu_p}{f} &= \lambda \\ \lambda &= \frac{\frac{2.8}{5 \; s}}{\frac{20}{50 \; s}} = \left(\frac{2.8 \; m}{5 \;s}\right) \left(\frac{50 \; s}{20}\right) = \boxed{1.4 \; m}\end{aligned}\)

Emacs 24.5.1 (Org mode 8.2.10)