SHOW WORK PLEASE!!! A radio transmitter is placed in the origin of a Cartesian c

Question

SHOW WORK PLEASE!!!

A radio transmitter is placed in the origin of a Cartesian coordinate system and emits a signal at angular frequency omega_0. the signal from the transmitter travels freely along the positive x direction until it reaches a wall, at a distance L from the origin. the wall reflects the radio signal back toward the origin. You are walking, with a radio receiver, from the wall to the transmitter: What is the wavelength of the transmitted signal? Find the distance x_b from the origin at which you encounter the first maximum of interference. Find the distance x_c from the origin at which you encounter the first minimum of interference. How many maxima of interference do you encounter by the time you reach the transmitter? Assume that the signal wavelength is significantly shorter than the distance between the transmitter and the wall.

Explanation / Answer

part a:

angular frequency=w0

frequency=angular frequency/(2*pi)=w0/(2*pi)

speed =c (speed of light)

then wavelength=speed /frequency

=c/(w0/(2*pi))=2*pi*c/w0

part b:

maximum of interference occurs when path difference is integral multiple of wavelength.

at a distance xb from origin:

path difference between the two waves (one wave is directly emitted from the radio transmitter and second wave is reflected from the wall)

=(L+L-xb)-xb

=2*(L-xb)

for first maxima, 2*(L-xb)=wavelength=2*pi*c/w0

==>xb=L-(pi*c/w0)

part c:

for minima, path difference should be odd integral multiple of 0.5*wavelength

so for first minima:

2*(L-xc)=0.5*wavelength=0.5*2*pi*c/w0

==>L-xc=0.5*pi*c/w0

==>xc=L-(0.5*pi*c/w0)

part d:

minimum value of xb is 0 at which last of the maxima interference occur

hence if there are n interferences,

L-(n*pi*c/w0)=0

==>n=L*w0/(pi*c)

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

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