1. Travel time around the Earth. Calculate the approximate time it
takes for an electromagnetic signal to travel around the circumference
of the Earth. Assume the Earth to be a perfect sphere with an average
diameter of 1.274 × 104 km. Get solution
2. Travel time between the Earth and the Moon. The average distance from Earth to the Moon is 384,400 km. How long will it take an electromagnetic wave to travel this distance? Get solution
3. Earth–Moon communication. During the Moon landing of one of the Apollo spaceflights, a spoken message from Earth is heard returning to Earth approximately 2.7 seconds later. The message signal traveled from Earth to the Moon, from the earphone to the microphone attached to the astronaut’s space helmet, and back to Earth.25. Use this time delay to estimate a rough value for the speed of light. Get solution
4. Time delay of a radar signal. Radars use radio waves to determine the distance to a target. Radar systems consist of a transmitting antenna that emits a radio pulse, and a receiving antenna that measures the (typically small) reflected component of the emitted waves. If the transmitter and receiver are co-located, and if the receiver detects the pulses reflected from a target 40 μs after the radar pulses leave the transmitter, what is the distance of the target from the radar? Get solution
5. Echo from a cliff. A man shouts in the direction of a cliff, which causes an echo that he hears 3 seconds later. If sound travels in air at 340 m-s−1, how far away is the cliff? Get solution
6. Sonar. Sonar stands for SOund NAvigation and Ranging and is a device that uses reflected sound waves to measure underwater depths. A ship sends a sonar signal downward into the ocean and receives a return signal 6 seconds later. Assuming the speed of sound waves to be the same at all depths given by 1.5 × 103 m-s−1, how deep is the ocean at that location? Get solution
7. Sonar. It takes a sonar pulse 3.7 seconds to return to its ship after being transmitted vertically towards the ocean floor. Assuming a constant speed of 1.5 km-s−1, what is the depth of the ocean at this point? Get solution
8. Auto-focus camera. An auto-focus camera can focus on objects by use of an ultrasonic sound wave. Just like radar, the camera sends out sound waves which reflect off the distant objects and return back to the camera. A sensor detects the time it takes for the waves to return and then determines the distance of the object from the camera. If an ultrasonic sound wave returns to the camera 0.1 second after leaving the camera, how far is the object from the camera? Assume speed of the ultrasonic sound wave to be 340 m-s−1. (Polaroid developed an ultrasonic autofocus system that used 50 kHz waves, well outside the human hearing range of 20. Hz–20 kHz. Modern autofocusing cameras typically use reflected infrared light to triangulate objects in the field of view.) Get solution
9. Lightning and thunder. If a person heard the sound of a thunder approximately 5 seconds after observing the lightning flash at a distance, how far away from this person did the lightning strike? Assume the speed of sound to be 340 m-s−1. Get solution
10. A light-year. A light-year (ly) is a unit of distance and is defined as the distance that light can travel in 1 year. Find the equivalent of 1 light-year in kilometers. Get solution
11. A light-nanosecond. What is 1 light-nanosecond in meters? Get solution
12. 1. Astronomical Unit. The average distance between the Earth and the Sun is defined as 1. Astronomical Unit (AU) is about 1.5 × 108 km. What is 1. AU in light-seconds? Get solution
13. Distance between Proxima Centauri and Earth. The distance between Proxima Centauri, the nearest known star to Earth (besides our Sun), is about 4 × 1013 km. Find this distance in light years. Get solution
14. Seismic waves. A geological disturbance in California is detected at a seismograph station in Washington approximately 900 km away from the epicenter of the earthquake. If the seismic wave traveled at an average speed of 5 km-s−1, determine the time delay between the epicenter and seismograph station. Get solution
15. Tsunami waves. Tsunami is a Japanese word. It means harbor (“tsu”) waves (“nami”). Tsunamis are fairly common in Japan and caused many thousands of deaths in recent centuries. A massive earthquake hit the Pacific Ocean near Honshu, Japan in 2011 producing a tsunami wave which reached Crescent City, California about 10 hours later. If the distance between the epicenter of the earthquake and Crescent City is about 8020 km, determine the average speed of the tsunami wave. Get solution
16. The Indian Ocean tsunami. The Indian Ocean tsunami triggered by a massive underwater earthquake that occurred in 2004 devastated the shores of Indonesia, Sri Lanka, India, Thailand, and other countries with waves up to 15 m high, even reaching as far as the east coast of Africa. The epicenter of the earthquake was about 160 km west of Sumatra, Indonesia and 4500 km from Africa. Assuming the average speed of the tsunami to be 800 km per hour, approximately how long did it take for the tsunami to travel from the epicenter to Sumatra? How about to Africa? Get solution
17. Micro-bats. Micro-bats use a form of radar called echolocation to navigate and find their prey such as flying insects. They locate the surrounding objects by bouncing sound wave pulses off these objects and detecting the time delay between the emitted pulses and the reflected pulses. Determine the time delay between the pulse emitted by the micro-bat and the detected pulse reflected from an insect located 10 m away from the micro-bat. Assume the approximate speed of sound waves to be 340 m-s−1. Get solution
18. Overhead power lines. The alternating current (ac) high-voltage overhead power lines in most countries in the world operate at a standard frequency of 50. Hz. Assuming propagation at the speed of light, determine the maximum line length for lumped analysis. Get solution
19. Maximum path length. Consider an electrical signal path in a high-speed digital circuit application to carry signals with rise times as low as 250 ps. If the speed of propagation is v = c/3, determine the maximum path length for lumped-circuit analysis. Get solution
20. Maximum coax length. Consider a commercial coaxial cable with v = 2 × 108 m-s−1. If this cable is to be used at frequencies around 900. MHz, what is the maximum cable length for lumped-circuit analysis? Get solution
21. Travel time of a microstrip transmission line. What is the one-way travel time of a 9 cm long microstrip transmission line with v = 1.7 × 108 m-s−1? Get solution
22. Maximum cable length. A ham radio operator connects his 30. MHz transmitter to an antenna using a coaxial cable. Assuming the speed of propagation along the cable to be 2 × 108 m-s−1, determine the maximum coaxial cable length beyond which it can’t be modeled as a lumped-circuit element. Get solution
23. Microstrip transmission line. A 6 cm long microstrip signal trace with speed of propagation v = 2c/3 is to be used to carry 1 ns rise time signals. Is it appropriate to neglect transmission line effects and use lumped circuit analysis? Get solution
24. Stripline transmission line. A 12 cm long stripline transmission line having a speed of propagation v = c/2 is used to carry digital signals with 0.5 ns rise time. Is it appropriate to consider transmission line effects in this case? Get solution
25. On-chip GaAs interconnect. Consider an on-chip GaAs interconnect with speed of propagation v = 8 × 107 m-s−1 to be used to carry a digital signal with rise time tr = 50 ps. What is the maximum interconnect length for lumped-circuit analysis? Get solution
26. A coaxial cable-lumped or distributed analysis? A coaxial cable of length 10 m having a speed of propagation v = 0.75c is used to connect the antenna and the receiver of a microwave communication system. Assuming sinusoidal steady state, what is the highest frequency for lumped-circuit analysis? Get solution
2. Travel time between the Earth and the Moon. The average distance from Earth to the Moon is 384,400 km. How long will it take an electromagnetic wave to travel this distance? Get solution
3. Earth–Moon communication. During the Moon landing of one of the Apollo spaceflights, a spoken message from Earth is heard returning to Earth approximately 2.7 seconds later. The message signal traveled from Earth to the Moon, from the earphone to the microphone attached to the astronaut’s space helmet, and back to Earth.25. Use this time delay to estimate a rough value for the speed of light. Get solution
4. Time delay of a radar signal. Radars use radio waves to determine the distance to a target. Radar systems consist of a transmitting antenna that emits a radio pulse, and a receiving antenna that measures the (typically small) reflected component of the emitted waves. If the transmitter and receiver are co-located, and if the receiver detects the pulses reflected from a target 40 μs after the radar pulses leave the transmitter, what is the distance of the target from the radar? Get solution
5. Echo from a cliff. A man shouts in the direction of a cliff, which causes an echo that he hears 3 seconds later. If sound travels in air at 340 m-s−1, how far away is the cliff? Get solution
6. Sonar. Sonar stands for SOund NAvigation and Ranging and is a device that uses reflected sound waves to measure underwater depths. A ship sends a sonar signal downward into the ocean and receives a return signal 6 seconds later. Assuming the speed of sound waves to be the same at all depths given by 1.5 × 103 m-s−1, how deep is the ocean at that location? Get solution
7. Sonar. It takes a sonar pulse 3.7 seconds to return to its ship after being transmitted vertically towards the ocean floor. Assuming a constant speed of 1.5 km-s−1, what is the depth of the ocean at this point? Get solution
8. Auto-focus camera. An auto-focus camera can focus on objects by use of an ultrasonic sound wave. Just like radar, the camera sends out sound waves which reflect off the distant objects and return back to the camera. A sensor detects the time it takes for the waves to return and then determines the distance of the object from the camera. If an ultrasonic sound wave returns to the camera 0.1 second after leaving the camera, how far is the object from the camera? Assume speed of the ultrasonic sound wave to be 340 m-s−1. (Polaroid developed an ultrasonic autofocus system that used 50 kHz waves, well outside the human hearing range of 20. Hz–20 kHz. Modern autofocusing cameras typically use reflected infrared light to triangulate objects in the field of view.) Get solution
9. Lightning and thunder. If a person heard the sound of a thunder approximately 5 seconds after observing the lightning flash at a distance, how far away from this person did the lightning strike? Assume the speed of sound to be 340 m-s−1. Get solution
10. A light-year. A light-year (ly) is a unit of distance and is defined as the distance that light can travel in 1 year. Find the equivalent of 1 light-year in kilometers. Get solution
11. A light-nanosecond. What is 1 light-nanosecond in meters? Get solution
12. 1. Astronomical Unit. The average distance between the Earth and the Sun is defined as 1. Astronomical Unit (AU) is about 1.5 × 108 km. What is 1. AU in light-seconds? Get solution
13. Distance between Proxima Centauri and Earth. The distance between Proxima Centauri, the nearest known star to Earth (besides our Sun), is about 4 × 1013 km. Find this distance in light years. Get solution
14. Seismic waves. A geological disturbance in California is detected at a seismograph station in Washington approximately 900 km away from the epicenter of the earthquake. If the seismic wave traveled at an average speed of 5 km-s−1, determine the time delay between the epicenter and seismograph station. Get solution
15. Tsunami waves. Tsunami is a Japanese word. It means harbor (“tsu”) waves (“nami”). Tsunamis are fairly common in Japan and caused many thousands of deaths in recent centuries. A massive earthquake hit the Pacific Ocean near Honshu, Japan in 2011 producing a tsunami wave which reached Crescent City, California about 10 hours later. If the distance between the epicenter of the earthquake and Crescent City is about 8020 km, determine the average speed of the tsunami wave. Get solution
16. The Indian Ocean tsunami. The Indian Ocean tsunami triggered by a massive underwater earthquake that occurred in 2004 devastated the shores of Indonesia, Sri Lanka, India, Thailand, and other countries with waves up to 15 m high, even reaching as far as the east coast of Africa. The epicenter of the earthquake was about 160 km west of Sumatra, Indonesia and 4500 km from Africa. Assuming the average speed of the tsunami to be 800 km per hour, approximately how long did it take for the tsunami to travel from the epicenter to Sumatra? How about to Africa? Get solution
17. Micro-bats. Micro-bats use a form of radar called echolocation to navigate and find their prey such as flying insects. They locate the surrounding objects by bouncing sound wave pulses off these objects and detecting the time delay between the emitted pulses and the reflected pulses. Determine the time delay between the pulse emitted by the micro-bat and the detected pulse reflected from an insect located 10 m away from the micro-bat. Assume the approximate speed of sound waves to be 340 m-s−1. Get solution
18. Overhead power lines. The alternating current (ac) high-voltage overhead power lines in most countries in the world operate at a standard frequency of 50. Hz. Assuming propagation at the speed of light, determine the maximum line length for lumped analysis. Get solution
19. Maximum path length. Consider an electrical signal path in a high-speed digital circuit application to carry signals with rise times as low as 250 ps. If the speed of propagation is v = c/3, determine the maximum path length for lumped-circuit analysis. Get solution
20. Maximum coax length. Consider a commercial coaxial cable with v = 2 × 108 m-s−1. If this cable is to be used at frequencies around 900. MHz, what is the maximum cable length for lumped-circuit analysis? Get solution
21. Travel time of a microstrip transmission line. What is the one-way travel time of a 9 cm long microstrip transmission line with v = 1.7 × 108 m-s−1? Get solution
22. Maximum cable length. A ham radio operator connects his 30. MHz transmitter to an antenna using a coaxial cable. Assuming the speed of propagation along the cable to be 2 × 108 m-s−1, determine the maximum coaxial cable length beyond which it can’t be modeled as a lumped-circuit element. Get solution
23. Microstrip transmission line. A 6 cm long microstrip signal trace with speed of propagation v = 2c/3 is to be used to carry 1 ns rise time signals. Is it appropriate to neglect transmission line effects and use lumped circuit analysis? Get solution
24. Stripline transmission line. A 12 cm long stripline transmission line having a speed of propagation v = c/2 is used to carry digital signals with 0.5 ns rise time. Is it appropriate to consider transmission line effects in this case? Get solution
25. On-chip GaAs interconnect. Consider an on-chip GaAs interconnect with speed of propagation v = 8 × 107 m-s−1 to be used to carry a digital signal with rise time tr = 50 ps. What is the maximum interconnect length for lumped-circuit analysis? Get solution
26. A coaxial cable-lumped or distributed analysis? A coaxial cable of length 10 m having a speed of propagation v = 0.75c is used to connect the antenna and the receiver of a microwave communication system. Assuming sinusoidal steady state, what is the highest frequency for lumped-circuit analysis? Get solution
