Question

  A person with a radio-wave receiver starts out equidistant from two FM radio transmitters A and B that are 11.0 m apart, each one emitting in-phase radio waves at 93.0 MHz . She then walks so that she always remains 50.0 m from transmitter B. (See (Figure 1).) Limit your solution to the cases where 50.0m?x?65.0m.

part a)

For what values of x will she find the radio signal to be maximally enhanced?

Express your answers in increasing order to three significant figures, separated by commas.

part b)

For what values of x will she find the radio signal to be cancelled?

Express your answers in increasing order to three significant figures, separated by commas.

Answer 1

as c=3*10^8m/s

?= (3*10^8)/(93*10^6)= 3.22 m

Constructive interference : abs(L1-L2)=n? -> L1=L2+n?

n=0: x= 50+0= 50 [m]

n=1: x= 50+1*3.22= 53.22 [m]

n=2: x= 50+2*3.22= 56.44 [m]

n=3: x= 50+3*3.22= 59.66[m]

n=4: x= 50+4*3.22= 62.88 [m]

Destructive interference : abs(L1-L2)=(n+1/2)? -> L1=L2+(n+1/2)?

n=0: x= 50+(0+1/2)*3.22= 51.61 [m]

n=1: x= 50+(1+1/2)*3.22= 54.83 [m]

n=2: x= 50+(2+1/2)*3.22= 58.05 [m]

n=3: x= 50+(3+1/2)*3.22 = 61.27 [m]

n=4: x= 50+(4+1/2)*3.22= 64.49 [m]