A spacecraft in orbit around the moon measures its altitude

A spacecraft in orbit around the moon measures its altitude by reflecting a pulsed 10 MHz radio signal from the surface. If the spacecraft is 65 km high, what is the time between the emission of the pulse and the detection of the echo?

217 µs

433 ns

433 µs

217 ns

2.The electromagnetic waves that carry FM radio range in frequency from 87.9 MHz to 107.9 MHz. What is the range of wavelengths of these radio waves?

500 - 750 nm

0.87 - 91.08 m

2.78 - 3.41 m

278 - 341 m

234 - 410 km

3. Communication with submerged submarines via radio waves is difficult because seawater is conductive and absorbs electromagnetic waves. Penetration into the ocean is greater at longer wavelengths, so the United States has radio installations that transmit at 90 Hz for submarine communications. What is the approximate wavelength of those extremely low frequency waves? 750 km

1500 km

3000 km

375 km

Solution

Speed of pulse wave = c = 3 x 10^8 m/s

t = 2h/c = (2 x 65 x 10^3 m ) / (3 x 10^8 ) = 433.33 x 10^-6 s = 433.33 us

--------------------------

wavelength = speed / frquency

for f = 87.9 MHz = 87.9 x 10^6 Hz

lambda = (3 x 10^8) / (87.9 x 10^6) = 3.41 m

for f = 107.9 MHz = 107.9 x 10^6 Hz

lambda = (3 x 10^8) / (107.9 x 10^6) = 2.78 m

Range = 2.78 - 3.41 m

---------------------

wavelength = c / f = (3 x 10^8 ) / (90 ) = 3.33 x 10^6 m Or 3.333 x 10^3 km

= 3333 km

Or approax 3000 km