Physics 21Fall, 2004Solution to HW-19Problem 1A wave on a string travels at 5 m/s towardthe right (labeled the positivexdirection). The transversedisplacement of the string at a point arbitrarily labeledx= 0is observed to bey0(t) = 0.03e−0.6tcos(50t),wheretis in seconds andyis in meters.(a) What is themathematical expression for the traveling wave on the stringas a function ofxandt?(b) Answer part (a) for a wavemoving toward the left rather than toward the right.Replacetbyt±x/v, using the upper (lower) sign forpropagation to the left (right):y0(x, t) = 0.03 exp−0.6t±xvcos 50t±xvForv= 5 m/s,y0(x, t) = 0.03 exp [−0.6t∓0.12x] cos [50t±10x].Problem 2What is the frequency of yellow light with awavelength of 5.9×10−7m in empty space?λf=c⇒f=c/λ=3×1085.9×10−7= 5.1×1014HzProblem 3The mathematical expression for a travelingwave on a string is given byy(x, t) = 0.03 sin(40πt+ 8πx)wherexandyare in meters,tis in seconds, andx≥0. (a)In what direction does the wave propagate?
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