Detailed explanation is highly appreciated! The pattern of sound waves emitted b

Question

Detailed explanation is highly appreciated!

The pattern of sound waves emitted by a source traveling at constant velocity is shown in the animation below. The source in the animation travels at a speed of 50% of the speed of the waves in the medium. At rest, the source emits a frequency of 360 Hz. The small rectangle in the animation represents an observer. If the source travels toward the observer at a constant velocity of 27.0% of the speed of the waves in the medium, what is the frequency of the waves observed by the observer? Hz After the source passes the observer, what is the frequency of the waves observed by the observer? Hz

Explanation / Answer

x6y +y6x =6

product rule (uv)'=u'v +uv'

derivative of pn=npn-1

differentiate with respect to x on both sides

[(6x6-1 dx/dx)y +x6(dy/dx)] + [(6y6-1dy/dx)x + y6(dx/dx)]    =d6 /dx

[(6x5)y +x6(dy/dx)] + [(6y5dy/dx)x + y6]    =0

[(6yx5) +x6(dy/dx)] + [(6xy5dy/dx) + y6]    =0

(x6+6xy5)(dy/dx)=-(6yx5+y6)

(dy/dx)=-(6yx5+y6)/(x6+6xy5)

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