Two radio antennas separated by d = 271 m, as shown in the figure below, simulta

Question

Two radio antennas separated by d = 271 m, as shown in the figure below, simultaneously transmit identical signals of the same wavelength. A radio in a car traveling due north receives the signals.

(a) If the car is at the position of the third maximum, what is the wavelength of the signals?


(b) How much farther must the car travel to encounter the next minimum in reception? (Hint: Determine the path difference between the two signals at the two locations of the car.)

Your response differs from the correct answer by more than 100%. m

Explanation / Answer

a.)tan(theta)=400/1000

So theta=21.8

d*sin(theta)=m*lambda

m=4

lambda=d*sin(theta)/4=271*sin(21.8)/4= 25.160 m

b.) d sin(theta) = (m + 1/2 ) *lambda

m=4

d*sin(theta)=9*lambda/2

sin(theta)=9*lambda/2d=9*25.160/(2*271)= 0.4178

So theta(min)=24.7

tan(theta)=y(min)/1000

So y(min)=tan(24.7)*1000= 459.9 m

So, the car will have to move additional 459.9 - 400 = 59.9 m

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.