Question

Standing wave can be represented as a product of two periodic functions (spatial and tem- poral). Consider the following superpositions of waves: VA(2, t) = A sin(kx – wt) + 2A sin(kx + wt) VB(x, t) = A sin(kx – wt) + A cos(kx + wt) wc(,t) = A sin(kx - wt) + A sin(kx + 2wt) Does either of them (WA, VB and/or vc) correspond to a standing wave? Use trigonometric identities to combine the terms and evaluate the results. Show the results together with a final answer (yes/no).

Answer 1

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NOTE : The identities used in this solution are:

Sin( A+B)=Sin A CosB+ Sin B Cos A

Sin( A-B)=Sin A CosB - Sin B Cos A

Cos( A+B)=Cos A CosB- Sin B Sin A

Cos( A-B)=Cos A CosB + Sin B Sin A

Sin C+ Sin D = 2 Sin(C+D)/2 Cos (C-D)/2

Sin C-Sin D = 2 Cos(C+D)/2 Sin (C-D)/2 etc