1) A Wi-Fi system operating at 5.0 GHz calls for an antenna a half wavelength lo

Question

1) A Wi-Fi system operating at 5.0 GHz calls for an antenna a half wavelength long.How long should the antenna be?

2) An airplane's two engines are supposed to be turning at 520 rpm, and one of them is. Yet, as a passenger in the plane, you hear the engines' sound intensify every 6.0 s.

Find a possible value for the rotational speed of the second engine. Express your answer numerically. If there is more than one value, enter each value separated by a comma.

3) The stationary siren on a firehouse is blaring at87.0 Hz, which a firefighter racing toward the station perceives as 99.2 Hz.At what speed is the firefighter approaching the station?

Explanation / Answer

1) frequency = 5 GHz

frequency = 5 *10^9 Hz

wavelength = speed of wave/frequency

wavelength = 3 *10^8/5 *10^9

wavelength = 0.06 m

length of antenna = wavelength/2

length of antenna = 0.03 m

2)

frequency of plane 1 , f1 = 520 rpm

frequency of plane 2 , f2

sound beat frequency , f = 60/6 s

f = 10 rpm

beat = |f1 - f2|

10 = |520 - f2|

f2 = 510 rpm , 530 rpm

3)let the speed of firefighter is v

f = f0 * (v + vs)/vs

99.2 = 87 * (v + 343)/343

solving for v

v = 48.1 m/s

the speed of firefighter is 48.1 m/s

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