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Problems on wave motion, beats, standing waves

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On quiz 2 below please explain 1-5 better and 7 - 10 better, specifically, what equations are used to solve each question, how are the numbers and equations worked out to see better. Please do the same for quiz 3 for problems 1-7.

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Please refer the attachment for solution.




The general equations of a traveling wave is :
y = A sin[(2Π/λ)x + (2Π/T)t] ....(1)

where : A = amplitude, T = time period, λ = wave length, - sign represents the wave traveling in positive direction (forward) and + sign implies wave traveling in negative direction (backwards).

Alternative forms of the above equations are :

y = A sin[kx + ωt] ....(2)

where : ω = 2Π/T = angular frequency and k = 2Π/λ = wave number (unit m-1)

or y = A sin2Π/λ[x + vt] .......(3) [arrived at by taking 2Π/λ out of the brackets and noting that λ/T = velocity]

where : v = velocity of the wave

In the present case the equation of the wave is given as : y = 4(cm) sin(5Πx + 12Πt) ...(4)

1. ...

Solution Summary

This set of problems includes good examples illustrating wave motion, beats and standing waves.