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# General Physics (Calculus) PHY 212

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This 3 page Class Notes was uploaded by Wilson Gibson V on Monday October 19, 2015. The Class Notes belongs to PHY 212 at Portland Community College taught by Staff in Fall. Since its upload, it has received 16 views. For similar materials see /class/224631/phy-212-portland-community-college in Physics 2 at Portland Community College.

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Date Created: 10/19/15

Phy 212 General Physics II 7142010 Chapter 16 Worksheet Waves I Traveling Waves 1 A particular wave traveling along a string is described by yxt 00060msin0006x 600t a How much time does any particular point in the string take to move between the displacements y2 mm and y2 mm Ans There 2 interpretations to this problem Interpretation 1 v The period T for this wave is T2l00105 s 0 2 mm The dIspIacement from 2mm to 2mm IS 12 A and therefore the time elapsed is 2 mm t I 000525 5 2 Interpretation 2 This one is more complex The phase difference s V between 2mm to 2mm is 2 mm 00040m 7139 7r 00120m 3 2 mm The tIme elapsed IS related to perIod T by If t 3 27 7 3 t I 00018 s T 27 27 6 b Determine the amplitude frequency period and wave speed for this traveling wave Ans ym00060 m f3955 Hz T 3 00105 s and v 9 105x105g 27 f k c What is the equation for the transverse velocity of any particular point along the string rn 39 rad rad Ans v a 36sm0006x 600t d What is the maximum transverse velocity of any particular point along the string Ans vrn mym 36 ms 2 A sinusoidal wave of frequency 500 Hz has a speed of 350 ms a How far apart are 2 points that differ in phase by 113 radians Ansl 07m 3 3 Ax0117m 500Hz Ax g 3 b What is the phase difference between 2 displacements at a certain point at times 1000 ms apart 00025 3 A 0390015 Ans T 0002 s 27 73 nrad 500HZ Phy 212 General Physics II 7142010 Chapter 16 Worksheet Waves I 2 Waves on a Stretched String 3 The linear density of a string is 15X10394 kgm The equation of a transverse wave on a string is YXt 0025msin20fnJx 309 a What is the wave speed m Ans v9 305 15m k 20 s b What is the tension in the string Ans FT W2 15x10394152 00338 N c What is the average power for this wave Ans P 12uv02ym2 000064 w 4 The equation of a transverse wave on a string is yXt 20mmsin20x 600t The tension in the string is 15 N a What is the wave speed Ansv96005 m k 20 s b What is the linear mass density of the string in grams per meter Ans u F42 15N2 167X10392 v 30 c Determine the average power transmitted by this wave Ans P 12uv02ym2 036 w 62y i62y d Demonstrate that this transverse wave satisfies the wave equation a 2 2 atz X v The Wave Equation 5 Consider the following wave yXt 005msin50rad X 10t a Verify that this wave satisfies the wave equation 2 X 62y ra 39 ra ra 39 39 ra ra Ans 6X2 50d2005msn50x10gt 125m1Sn50X10t v2 at2 2m 5 Lazy Wsin50Xlot 125m 1sin50X1Ot Phy 212 General Physics II 7142010 Chapter 16 Worksheet Waves I 3 b Use the wave equation to determine the speed of the wave Ans Setting the above equations together and not assuming a priori that v wk leads to 10m 2 005m w 502005m 3 vJv2 10 fad 20m v 50 c Calculate the frequency wavelength and period for this wave Ans ym005 m f3159 Hz1 L 0796 m and T 3 0629 s 27139 27139 f d Consider a 2quotd wave with same frequency and wavelength traveling in the same direction where yZmaX 001 m and dpz 113 Construct a phasor diagram for the combined waves H S nunuuuuuyu nununuunuu gt YZ Y1 e What is the amplitude of the resultant wave Ans y39 yf y ZylyzcosnJ 00557 m Standing Waves 7 A string is attached to a string vibrator f120 Hz at one end and fixed at the other The length of the string is 12 m a What wavelengths will satisfy the standing wave condition for the string 1 Ans L n j where n123 etc b What is the maximum wave speed that will produce a standing wave in this string Ans For the same frequency the greatest wavelength will produce the maximum speed when n1 2 27 24 m and v M 24 m120 Hz 288g c What string tension will correspond to the wave in b is the linear density of the string is 25x10394 kgm Ans FT W2 25x103942882 207 N d What string tension would correspond to a standing wave that produces 6 nodes in the string Ans For 6 nodes n5 1 048 m and v if 048 m120 Hz 576 The tension in the string would be FT szZ 25x10394 k g5762 0829 N

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