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Determining Wave Speed

Determining Wave Speed. Section 8.4. Key Terms. Universal Wave Equation Linear Density. Universal Wave Equation. To determine the how fast a wave is moving, you must know: Its period ( eg – time between successive crests passing a reference point) Its wavelength (distance between crests)

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Determining Wave Speed

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  1. Determining Wave Speed Section 8.4

  2. Key Terms • Universal Wave Equation • Linear Density

  3. Universal Wave Equation • To determine the how fast a wave is moving, you must know: • Its period (eg – time between successive crests passing a reference point) • Its wavelength (distance between crests) • You can then calculate wave speed using the equation for average speed: • Or, for wave speed

  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 220.0 Hz. Calculate its wave speed. Given: = 2.3 m; f = 220.0 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 1046.50 Hz. Calculate the wavelength of the sound wave. Given: v= 350 m/s; f = 1046.50 Hz Required:= ? Analysis: = v/f Solution: = (350 m/s) / (1046.50 Hz) = 0.33 m Statement: The wave speed on the string is 0.33 m

  7. Practice Questions 1-3 • 530 m/s • 140 m • 2.0 x 102 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 • FT = 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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