A)The resultant of two interfering waves of the same wavelength and frequency is

Question

A)The resultant of two interfering waves of the same wavelength and frequency is given as y'=(14mm)*sin(kx+wt+.5rad) One of the interfering waves is y1=(8mm)*sin(kx+wt). Calc the amplitude and phase constant of the other interfering wave and perform the calculations to obtain this amplitude and phase constant. Write the equation of this interfering wave.

B)Sound of a single frequency is sent into the system of pipes, one straight, the other consisting of two semi-circular paths of radii 20cm and 30cm. What is the lowest frequency that produces an intensity maximum on the output side?

Explanation / Answer

let the eq. of 2nd wave be y2=(amm)*sin(wt+kx+b)

then vectorially we have

14*cos(90/pi)=8+acosb

14*sin(90/pi)=asinb

solving above two equations we get

a=7.964 and b=1rad

the eq. of the interfering wave is y2=(7.964mm)sin(kx+wt+1rad)

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