16.5 The electromagnetic spectrum  (Page 8/19)

Radio station WWVB, operated by the National Institute of Standards and Technology (NIST) from Fort Collins, Colorado, at a low frequency of 60 kHz, broadcasts a time synchronization signal whose range covers the entire continental US. The timing of the synchronization signal is controlled by a set of atomic clocks to an accuracy of $1\times {10}^{\mathrm{-12}}\text{s},$ and repeats every 1 minute. The signal is used for devices, such as radio-controlled watches, that automatically synchronize with it at preset local times. WWVB’s long wavelength signal tends to propagate close to the ground.
(a) Calculate the wavelength of the radio waves from WWVB.
(b) Estimate the error that the travel time of the signal causes in synchronizing a radio controlled watch in Norfolk, Virginia, which is 1570 mi (2527 km) from Fort Collins, Colorado.

An outdoor WiFi unit for a picnic area has a 100-mW output and a range of about 30 m. What output power would reduce its range to 12 m for use with the same devices as before? Assume there are no obstacles in the way and that microwaves into the ground are simply absorbed.

7 . The prefix “mega” (M) and “kilo” (k), when referring to amounts of computer data, refer to factors of 1024 or $2^{10}$ rather than 1000 for the prefix kilo , and ${1024}^2=2^{20}$ rather than 1,000,000 for the prefix Mega (M). If a wireless (WiFi) router transfers 150 Mbps of data, how many bits per second is that in decimal arithmetic?

A computer user finds that his wireless router transmits data at a rate of 75 Mbps (megabits per second). Compare the average time to transmit one bit of data with the time difference between the wifi signal reaching an observer’s cell phone directly and by bouncing back to the observer from a wall 8.00 m past the observer.

(a) The ideal size (most efficient) for a broadcast antenna with one end on the ground is one-fourth the wavelength ( $\lambda \text{/}4$ ) of the electromagnetic radiation being sent out. If a new radio station has such an antenna that is 50.0 m high, what frequency does it broadcast most efficiently? Is this in the AM or FM band? (b) Discuss the analogy of the fundamental resonant mode of an air column closed at one end to the resonance of currents on an antenna that is one-fourth their wavelength.

What are the wavelengths of (a) X-rays of frequency $2.0\times {10}^{17}\text{Hz?}$ (b) Yellow light of frequency $5.1\times {10}^{14}\text{Hz?}$ (c) Gamma rays of frequency $1.0\times {10}^{23}\text{Hz?}$

For red light of $\lambda =660\text{nm}$ , what are f , $\omega$ , and k ?

A radio transmitter broadcasts plane electromagnetic waves whose maximum electric field at a particular location is $1.55\times {10}^{\mathrm{-3}}\text{V/m}.$ What is the maximum magnitude of the oscillating magnetic field at that location? How does it compare with Earth’s magnetic field?

(a) Two microwave frequencies authorized for use in microwave ovens are: 915 and 2450 MHz. Calculate the wavelength of each. (b) Which frequency would produce smaller hot spots in foods due to interference effects?