Question 19 of 21 The following two traveling waves are superposed to create a s

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Question 19 of 21 The following two traveling waves are superposed to create a standing wave: Map a ,= (2.9 cm) sin(0.25 cm-1)x-(8.5 s-1) 1) , (2.9 cm) sin((0.25 cm-')x+ (8.5 s-' )t For each question below, enter a number and choose the appropriate units. (a) What is the resulting amplitude of the standing wave? Number Select answer (b) What is the resulting wavelength of the standing wave? Number Select answer (c) What is the resulting angular frequency of the standing wave? Number Select answer Previous Give Up & View Solution O check Answer Next +1 Exit Hint

Explanation / Answer

y1 = A sin(kx - wt)
y2 = A sin(kx + wt) ,(w is the angular frequency).
Then :
y = y1+y2 = A{sin(kx - wt) + sin(kx + wt)}
and (sinp + sinq = 2 sin[(p+q)/2]*cos[(p-q)/2] )
y = 2 A sin(kx) cos(wt)=5.8sin0.25xcos8.5t

Amplitude wil be given by

y=2×2.9×sin0.25x=5.8sin0.25x

b)Wavelength

k=2×pi/wavelength

Wavelength =2×3.14/0.25=25.12cm

C) angular frequency =w=8.5s^-1

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