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DETERMINING WAVE SPEED Section 8.4. Key Terms  Universal Wave Equation  Linear Density.

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Presentation on theme: "DETERMINING WAVE SPEED Section 8.4. Key Terms  Universal Wave Equation  Linear Density."— Presentation transcript:

1 DETERMINING WAVE SPEED Section 8.4

2 Key Terms  Universal Wave Equation  Linear Density

3 Universal Wave Equation

4 Universal Wave Equation cont’d  Since frequency is the reciprocal of period, we can further develop the equation:

5 Sample Problem 1  A harp string supports a wave with a wavelength of 2.3 m and a frequency of Hz. Calculate its wave speed. Given: = 2.3 m; f = Hz Required: v = ? Analysis: v = f Solution: v = f = (220.0 Hz)(2.3 m) v = 506 m/s Statement: The wave speed on the string is 506 m/s

6 Sample Problem 2 A trumpet produces a sound wave that is observed travelling at 350 m/s with a frequency of Hz. Calculate the wavelength of the sound wave. Given: v = 350 m/s; f = Hz Required: = ? Analysis: = v/f Solution: = (350 m/s) / ( Hz) = 0.33 m Statement: The wave speed on the string is 0.33 m

7 Practice Questions m/s m x 10 2 Hz

8 Factors That Affect Wave Speed  Energy transfers much more efficiently using waves is more efficient if the particle vibrations do not absorb much energy.  An inflated soccer ball will bounce much more effectively than a deflated one.

9 Linear Density  The speed of a wave along a string is governed by the properties of the string.  Think guitar/violin strings.  A string’s linear density, µ (mass per unit distance), determines how much force it will take to make the string vibrate.  m = mass of string in kg, L = length in metres

10 String Tension  String tension will also affect wave speed  Loose strings vs. taut strings  F T = tension in the string, in newtons  µ = linear density, in kg/m

11 Sample Problem 1 A wave machine has a string of mass 350g and a length of 2.3m. What must the tension of the string be to send a wave along the string at a speed of 50.0 m/s? Practice questions 1-3

12 Summary  The universal wave equation relates the speed of a wave to its frequency and wavelength. The universal wave equation applies to all waves.  More rigid intermolecular forces allow for a faster transfer of energy, and therefore a higher wave speed in a medium.  Waves travel faster in hotter gases than in cooler gases because of the increased molecular motion caused by the higher temperature in a hotter gas.  The speed of a wave on a string depends on the linear density of the string and the string’s tension:

13 Homework  Page 391  Questions 1-7


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