Chapter 20

Chapter 20 - 20.1 Model The wave is a traveling wave on a...

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20.1. Model : The wave is a traveling wave on a stretched string. Solve: The wave speed on a stretched string with linear density μ is string S /. vT = The wave speed if the tension is doubled will be () S string string 2 2 2 200 m/s 283 m/s T vv == = =
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20.2. Model: The wave is a traveling wave on a stretched string. Solve: The wave speed on a stretched string with linear density μ is S string 75 N 150 m/s T v μμ =⇒ = 3 3.333 10 kg/m ⇒= × For a wave speed of 180 m/s, the required tension will be ( )( ) 2 23 Ss t r i n g 3.333 10 kg/m 180 m/s 110 N Tv ==× =
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20.3. Model: The wave pulse is a traveling wave on a stretched string. Solve: The wave speed on a stretched string with linear density μ is ( )( ) SS S string 3 2.0 m 20 N 2.0 m 0.025 kg 25 g 50 10 s TTL T vm m/L m m == = = = = ×
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20.4. Model: This is a wave traveling at constant speed. The pulse moves 1 m to the right every second. Visualize: The snapshot graph shows the wave at all points on the x -axis at t = 0 s. The wave is just reaching x = 5.0. The first part of the wave causes an upward displacement of the medium. The rising portion of the wave is 2 m wide, so it will take 2 s to pass the x = 5.0 m point. The constant part of the wave, whose width is 2 m, will take 2 seconds to pass x = 5.0 m and during this time the displacement of the medium will be a constant ( Δ y = 1 cm). The trailing edge of the pulse arrives at t = 4 s at x = 5.0 m. The displacement now becomes zero and stays zero for all later times.
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20.5. Model: This is a wave traveling at constant speed. The pulse moves 1 m to the left every second. Visualize: This snapshot graph shows the wave at all points on the x -axis at t = 2 s. You can see that the leading edge of the wave at t = 2 s is precisely at x = 0 m. That is, in the first 2 seconds, the displacement is zero at x = 0 m. The first part of the wave causes a downward displacement of the medium, so immediately after t = 2 s the displacement at x = 0 m will be negative. The negative portion of the wave pulse is 3 m wide and takes 3 s to pass x = 0 m. The positive portion begins to pass through x = 0 m at t = 5 s and until t = 8 s the displacement of the medium is positive. The displacement at x = 0 m returns to zero at t = 8 s and remains zero for all later times.
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20.6. Model: This is a wave traveling at constant speed to the right at 1 m/s. Visualize: This is the history graph of a wave at x = 0 m. The graph shows that the x = 0 m point of the medium first sees the negative portion of the pulse wave at t = 1.0 s. Thus, the snapshot graph of this wave at t = 1.0 s must have the leading negative portion of the wave at x = 0 m.
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20.7. Model: This is a wave traveling at constant speed to the left at 1 m/s. Visualize: This is the history graph of a wave at x = 2 m. Because the wave is moving to the left at 1 m/s, the wave passes the x = 2 m position a distance of 1 m in 1 s. Because the flat part of the history graph takes 2 s to pass the x = 2 m position, its width is 2 m. Similarly, the width of the linearly increasing part of the history graph is 2 m. The center of the flat part of the history graph corresponds to both t = 0 s and x = 2 m.
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20.8. Visualize : Figure EX20.8 shows a snapshot graph at
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This note was uploaded on 11/26/2010 for the course MTH 232 taught by Professor Smith during the Spring '10 term at UConn.

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Chapter 20 - 20.1 Model The wave is a traveling wave on a...

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