Question

chapter 24 part 2

1. What is the frequency of a 17.7 m wavelength radio wave?  Give your answe in MHz.

2. A 2.34 m diameter university communications satellite dish receives TV signals that have a maximum electric field strength (for one channel) of 7.51 μV/m. What is the power received by the dish in 10^-13 W?

3. A radio antenna can pick up wavelengths between 2.6 μm and 57.2 μm.  How much of the frequency spectrum in (in 10¹³ Hz) does this cover?

4. Lasers can be constructed that produce an extremely high intensity electromagnetic wave for a brief time—called pulsed lasers. They are used to ignite nuclear fusion, for example. Such a laser may produce an electromagnetic wave with a maximum electric field strength of 2.32×10¹¹ V / m for a time of 1.14 ns. What is the energy in kJ delivered on a 1.42 mm² area?

Answer 1

1)given,

lambda = 17.7 m

We know that, v = f lambda

f = v/lambda = 3 x 10^8/17.7 = 1.7 x 10^7 Hz

Hence, f = 1.7 x 10^7 Hz = 17 MHz

2)Given,

E = 7.51 x 10^-6 V/m ; d = 2.34 m => r = 1.17 m

We know that

Erms = Em/sqrt(2) = 7.51 x 10^-6/1.414 = 5.31 x 10^-6 V/m

Erms = sqrt (I/ce0)

Erms^2 = I/ce0

I = Erms^2 c e0

I = (5.31 x 10^-6)^2 x 3 x 10^8 x 8.85 x 10^-12 = 7.49 x 10^-14 W/m^2

I = P/A

P = IA = 7.49 x 10^-14 x 4 x 3.14 x 1.17^2 = 1.29 x 10^-12 W

Hence, P = 1.29 x 10^-12 W = 12.9 x 10^-13 W

3)f1 = 3 x 10^8/(2.6 x 10^-6) = 1.15 x 10^14 Hz

f2 = 3 x 10^8/(57.2 x 10^-6) = 5.24 x 10^12 Hz

between: 0.524 x 10^13 Hz ; 11.5 x 10^13 Hz