Question

# chapter 24 part 2 1. What is the frequency of a 17.7 m wavelength radio wave? ...

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?

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