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**Determining Wave Speed**

Section 8.4

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Key Terms Universal Wave Equation Linear Density

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**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: 𝑣= 𝑑 𝑡 Or, for wave speed

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**Universal Wave Equation cont’d**

Since frequency is the reciprocal of period, we can further develop the equation:

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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

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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

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Practice Questions 1-3 530 m/s 140 m 2.0 x 102 Hz

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**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.

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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

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**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

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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

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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:

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Homework Page 391 Questions 1-7

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