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(2) The ionosphere is a layer of air high up in Earth's atmosphere. In the ionosphere, the air density is so low and the high-energy ultraviolet radiation from the Sun is so intense, many of the air molecules are ionized. This makes the ionosphere reflective to short-wave radio waves. Because of this, a short-wave transmitter on the surface of Earth can radiate radio waves that reflect off the ionosphere, and then travel down to a radio receiver on Earth that is beyond the horizon of the transmitter. Since short-wave radio waves can travel around the world, they are often used for einergency broadcasts. Suppose the layer of the ionosphere where the reflection occurs is 160 km above the surface of Earth. There is no phase-reversal of the radio waves at this reflection. Suppose the short-wave radio waves being transmitted have a frequency of 3.00 MHz = 3.00 x 10 Hz, where 1 Hz = 1 Hertz = 1 cycle/s = 1/s. Suppose a fiber-optic cable lies on the surface of Earth. It stretches from the transmitter to the receiver, and has a length s. Assume Earth is a sphere of radius R= 6378 kn, ignoring bumps such as mountains or dents such as ocean trenches. Signals identical to the ones radiated by the short-wave transmitter also travel through this cable to the receiver. In the receiver, the short-wave radio waves that reflect off the ionosphere and the signals that travel through the cable are combined. (8) How many kilometers (kım) is the maximum distance s, from the transmitter to the receiver along the surface of Earth, at which a minimum of destructive iterference can occur when the short-wave signal and the signals through the cable are combined? Remember that s is not a straight line.

(2) The ionosphere is a layer of air high up in Earth's atmosphere. In the ionosphere, the air density is so low and the high-energy ultraviolet radiation from the Sun is so intense, many of the air molecules are ionized. This makes the ionosphere reflective to short-wave radio waves. Because of this, a short-wave transmitter on the surface of Earth can radiate radio waves that reflect off the ionosphere, and then travel down to a radio receiver on Earth that is beyond the horizon of the transmitter. Since short-wave radio waves can travel around the world, they are often used for einergency broadcasts. Suppose the layer of the ionosphere where the reflection occurs is 160 km above the surface of Earth. There is no phase-reversal of the radio waves at this reflection. Suppose the short-wave radio waves being transmitted have a frequency of 3.00 MHz = 3.00 x 10 Hz, where 1 Hz = 1 Hertz = 1 cycle/s = 1/s. Suppose a fiber-optic cable lies on the surface of Earth. It stretches from the transmitter to the receiver, and has a length s. Assume Earth is a sphere of radius R= 6378 kn, ignoring bumps such as mountains or dents such as ocean trenches. Signals identical to the ones radiated by the short-wave transmitter also travel through this cable to the receiver. In the receiver, the short-wave radio waves that reflect off the ionosphere and the signals that travel through the cable are combined. (8) How many kilometers (kım) is the maximum distance s, from the transmitter to the receiver along the surface of Earth, at which a minimum of destructive iterference can occur when the short-wave signal and the signals through the cable are combined? Remember that s is not a straight line.

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(2) The ionosphere is a layer of air high up in Earth's atmosphere. In the ionosphere, the air density is so low and the high-energy ultraviolet radiation from the Sun is so intense, many of the air molecules are ionized. This makes the ionosphere reflective to short-wave radio waves. Because of this, a short-wave transmitter on the surface of Earth can radiate radio waves that reflect off the ionosphere, and then travel down to a radio receiver on Earth that is beyond the horizon of the transmitter. Since short-wave radio waves can travel around the world, they are often used for einergency broadcasts. Suppose the layer of the ionosphere where the reflection occurs is 160 km above the surface of Earth. There is no phase-reversal of the radio waves at this reflection. Suppose the short-wave radio waves being transmitted have a frequency of 3.00 MHz 3.00 x 106 Hz, where 1 Hz =1 Hertz = 1 cycle/s= 1/s. %3D Suppose a fiber-optic cable lies on the surface of Earth. It stretches from the transmitter to the receiver, and has a length s. Assume Earth is a sphere of radius R 6378 km, ignoring bumps such as mountains or dents such as ocean trenches. Signals identical to the ones radiated by the short-wave transmitter also travel through this cable to the receiver. In the receiver, the short-wave radio waves that reflect off the ionosphere and the signals that travel through the cable are combined. (a) How many kilometers (km) is the maximum distance s, from the transmitter to the receiver along the surface of Earth, at which minimum of destructive interference can occur when the short-wave signal and the signals through the cable are combined? Remember that s is not a straight line. (b) How many km before this, along the surface of Earth on the path from the transmitter to the receiver, is the next minimum due to destructive interference? (c) How many km is the minimum distance s, from the transmitter and along the surface of Earth toward the receiver, at which destructive interference can occur between the two signals, for which m= 0? (d) How many km is the minimum distance s, from the transmitter and along the surface of Earth toward the receiver, at which destructive interference can occur between the two signals, for any value of m? (e) The ratio of the concentrations of carbon-14 to carbon-12 in a bone of a prehistoric person is 0.0623 times less than the ratio of the concentrations of carbon-14 to carbon-12 measured in a bone of a person who died less than a year ago. Carbon-12 is a stable isotope, but carbon-14 is radioactive, with a half-life of 5730 years. How many years old is the prehistoric bone? (The next page is blank, so you may write your answers there. You may also write answers on this page.)
Transcribed Image Text:(2) The ionosphere is a layer of air high up in Earth's atmosphere. In the ionosphere, the air density is so low and the high-energy ultraviolet radiation from the Sun is so intense, many of the air molecules are ionized. This makes the ionosphere reflective to short-wave radio waves. Because of this, a short-wave transmitter on the surface of Earth can radiate radio waves that reflect off the ionosphere, and then travel down to a radio receiver on Earth that is beyond the horizon of the transmitter. Since short-wave radio waves can travel around the world, they are often used for einergency broadcasts. Suppose the layer of the ionosphere where the reflection occurs is 160 km above the surface of Earth. There is no phase-reversal of the radio waves at this reflection. Suppose the short-wave radio waves being transmitted have a frequency of 3.00 MHz 3.00 x 106 Hz, where 1 Hz =1 Hertz = 1 cycle/s= 1/s. %3D Suppose a fiber-optic cable lies on the surface of Earth. It stretches from the transmitter to the receiver, and has a length s. Assume Earth is a sphere of radius R 6378 km, ignoring bumps such as mountains or dents such as ocean trenches. Signals identical to the ones radiated by the short-wave transmitter also travel through this cable to the receiver. In the receiver, the short-wave radio waves that reflect off the ionosphere and the signals that travel through the cable are combined. (a) How many kilometers (km) is the maximum distance s, from the transmitter to the receiver along the surface of Earth, at which minimum of destructive interference can occur when the short-wave signal and the signals through the cable are combined? Remember that s is not a straight line. (b) How many km before this, along the surface of Earth on the path from the transmitter to the receiver, is the next minimum due to destructive interference? (c) How many km is the minimum distance s, from the transmitter and along the surface of Earth toward the receiver, at which destructive interference can occur between the two signals, for which m= 0? (d) How many km is the minimum distance s, from the transmitter and along the surface of Earth toward the receiver, at which destructive interference can occur between the two signals, for any value of m? (e) The ratio of the concentrations of carbon-14 to carbon-12 in a bone of a prehistoric person is 0.0623 times less than the ratio of the concentrations of carbon-14 to carbon-12 measured in a bone of a person who died less than a year ago. Carbon-12 is a stable isotope, but carbon-14 is radioactive, with a half-life of 5730 years. How many years old is the prehistoric bone? (The next page is blank, so you may write your answers there. You may also write answers on this page.)
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