Question

A radar set emits a transverse wave pulse of frequency 10.0 x 109 Hz towards an airplane. The echo is detected after a time of 75.0 x 10-6 s. a) Sketch the situation. b) Sketch the shape of the pulse. c) Find the distance to the plane. d) Find the wavelength of the wave. (v = 3.00 x 108 m/s)

Answer 1

d = 2.25 10⁴ m and λ = 3 m

Step-by-step explanation:

a and b) the wave approximates it to a beam that goes directly to the plane and bounces in all directions, returning to the source and emission.

The incident pulse has a Gaussian form with an intensity Io, the reflected wave has a lower intensity, but the Gaussian form must be maintained, a little more enlarged by air dispersion and metal absorption

c) The speed of the wave is constant

v = d / t

d = v t

d = 3 10⁸ 75.0 10⁻⁶

d = 2.25 10⁴ m

Note that we do not take into account the speed of the plane because in much less than the speed of the wave

d) wave speed is related to wavelength and frequency

v = λ f

λ = v / f

λ = 3. 10⁸/10 10⁹

λ = 3 m

Answer 2

For a and c please see attached copy of the diagrams

c) 1.125×10⁴m

d) 2.25×10⁴m

Step-by-step explanation:

c) Distance to the plane using Echo is Velocity V=2×Distance (d)/Time

where d=velocity×time/2, =3.0×10⁸×75×10⁻⁶/2 = 1.125×10⁴m

d) Wavelength λ=v/f =3.0×10⁸/10.0×10⁹=2.25×10⁴m