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Mastering Wave Speed Equations: A Comprehensive Guide

Learn to calculate wave speed using the universal wave equation. Understand the factors influencing wave speed, such as temperature and linear density. Examples and quizzes included!

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Mastering Wave Speed Equations: A Comprehensive Guide

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  1. 8.4 – Determining Wave Speed

  2. The Universal Wave Equation Recall: to find speed, v = d t For a wave, d = length of wave, λ t = time for one cycle, T v = λ or v = λf (since 1/T = f) T

  3. Things to Note: • One vibration/cycle of the source → one complete wavelength. • the frequency of the source = The frequency of the wave • If the frequency of the source never changes then the frequency of the wave doesn’t either, even if the speed and wavelength change. • Speed and wavelength can change due to a medium change

  4. Example 1 The wavelength of a water wave in a ripple tank is 0.080 m. If the frequency of the wave is 2.5 Hz, what is its speed?

  5. Example 2 The period of a sound wave from a piano is 1.18 x 10-3 s. If the speed of the wave in the air is 3.4 x 102 m/s, what is its wavelength?

  6. Factors That Affect Wave Speed Temperature • In gases, higher temp = more efficient transfer of energy because molecules are vibrating faster Linear Density • Mass/unit of distance → determines amount of force needed to make string vibrate µ = m m – mass (kg) L L – length (m)

  7. Factors That Affect Wave Speed

  8. Example 3 If a string on a wave machine has a linear density of 0.011 kg/m and a tension of 250 N, what is the wave speed?

  9. Example 4 If a 2.5 m long string on the same wave machine has a tension of 240 N, and the wave speed is 300 m/s, what is the mass of the string?

  10. Homework pg 391 #1- 7 Quiz on Wednesday

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