let w = 2 pi f
let k = 2 pi/wavelength L
wave moving right toward mirror
y = a sin (wt - kx)
wave moving left from mirror
y = a sin (wt + kx)
sum
y = a (sin(wt-kx) + sin(wt+kx))
then
sin(a+b) and sin(a-b)formula (trig)
y = a[sinwtcoskx+coswtsinkx+sinwtcoskx-coswtsinkx]
y = 2a [ sin wt cos kx ]
this is a standing wave, not traveling
it is node where cos kx = 0
that is when
kx = pi/2
kx = -pi/2
or
x = (pi/2)/(2pi/L)
x = -(pi/2)/(2pi/L)
distance between = pi L / 2 pi = L/2
given L/2 = .015 m
distance = rate * time
.015 = 3*10^8 T
get T
frequency = 1/T
A small source O of electromagnetic waves is placed some distance from a plane metal reflector M. A receiver R, moving between O and M along the line normal to the reflector, detects successive maximum and minimum readings on the meter joined to it. (a) explain why these readings are obtained. (b) calculate the frequency of the source O if the average distance between successive minima is 1.5 cm and the speed of electromagnetic waves in air= 3.0 x 10^8 m/s.
1 answer