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Introductory Physics Homework Help
Displacement of a Transverse Wave on a String Question
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[QUOTE="craig.16, post: 3221468, member: 299914"] [h2]Homework Statement [/h2] Question 1 (a) The displacement of a transverse wave on a string is described by: y(x, t) = 0.01 sin(4x + 200t + [tex]\pi[/tex]), where all quantities are expressed in SI units. i) Determine values (with appropriate units) for the period, wavelength, and phase velocity of the wave. [3] ii) Determine from first principles the average kinetic energy per metre of this wave on a string of mass per unit length 5 × 10 -2 kg m-1. [h2]Homework Equations[/h2] y(x,t)=Asin(kx+[tex]\omega[/tex]t) E[SUB]k[/SUB]=1/2[/tex]mv[SUP]2[/SUP] [h2]The Attempt at a Solution[/h2] For part (i): period, t=2[tex]\pi[/tex]/[tex]\omega[/tex]=2[tex]\pi[/tex]/200=[tex]\pi[/tex]/100=0.0314 seconds (3dp) wavelength, [tex]\lambda[/tex]=2[tex]\pi[/tex]/k=2[tex]\pi[/tex]/4=[tex]\pi[/tex]/2= 1.57 m (3 sf) phase velocity, v=[tex]\omega[/tex]/k=200/4=50ms[SUP]-1[/SUP] For part (ii): E[SUB]k[/SUB]=1/2[/tex]mv[SUP]2[/SUP]=1/2[/tex](5*10[SUP]-2[/SUP])(1.57)(50)[SUP]2[/SUP]=98.1J Just need confirmation on whether the first part is correct. As for the second part it was a blatant guess by using the SI units and knowing the original equation for kinetic energy, so I need some help on this one if it is incorrect. Also how do you do a fraction on this properly? I tried the first one in the "Above and Below" section but that isn't right. Thanks in advance. [/QUOTE]
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Displacement of a Transverse Wave on a String Question
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