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Ch. 31 - Maxwell's Equations and Electromagnetic Waves
Giancoli Douglas - Physics for Scientists and Engineers 5th edition
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook
All textbooksGiancoli Douglas 5th editionCh. 31 - Maxwell's Equations and Electromagnetic WavesProblem 50
Chapter 30, Problem 50

Who will hear the voice of a singer first: a person in the balcony 50.0 km away from the stage (see Fig. 31–26), or a person 1800 km away at home whose ear is next to the radio listening to a live broadcast? Roughly how much sooner? Assume the microphone is a few centimeters from the singer and the temperature is 20℃.


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1
Determine the speed of sound in air at 20°C. The formula for the speed of sound in air is given by: v = 331 + 0.6T, where T is the temperature in Celsius. Substitute T = 20°C to calculate the speed of sound.
Calculate the time it takes for the sound to travel to the person in the balcony. Use the formula: t = d/v, where d is the distance (50.0 km) and v is the speed of sound calculated in the previous step.
Determine the time it takes for the radio signal to reach the person 1800 km away. Radio waves travel at the speed of light, which is approximately 3.00 × 108 m/s. Use the formula: t = d/c, where d is the distance (1800 km) and c is the speed of light.
Compare the two times calculated in the previous steps to determine who hears the singer first. Subtract the smaller time from the larger time to find the time difference.
Interpret the result: Explain why the person listening to the radio hears the singer first, emphasizing the difference in propagation speeds of sound and electromagnetic waves (radio waves).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Speed of Sound

The speed of sound is the rate at which sound waves travel through a medium, typically air. At 20°C, the speed of sound in air is approximately 343 meters per second. This speed can vary based on temperature, humidity, and the medium through which the sound is traveling. Understanding this concept is crucial for determining how long it takes for sound to reach different observers.
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Distance and Time Relationship

The relationship between distance, speed, and time is fundamental in physics, expressed by the formula: distance = speed × time. This means that for a given speed, the time taken for sound to travel a certain distance can be calculated. In this scenario, comparing the distances to the two listeners will help determine who hears the singer first and by how much time.
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Radio Transmission Delay

Radio transmission involves converting sound into electromagnetic waves, which travel at the speed of light, approximately 299,792 kilometers per second. This speed is significantly faster than the speed of sound. However, there may be a slight delay in the transmission process, which can affect the timing of when the radio listener hears the singer compared to the person in the balcony.
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Example 2
Related Practice
Textbook Question

A global positioning system (GPS) functions by determining the travel times for EM waves from various satellites to a moving GPS receiver on Earth (car or hiker). If the receiver is to detect a change in the receiver’s position on the order of 3 m, what is the associated change in travel time (in ns) that must be measured?

Textbook Question

Compare 1030 on the AM dial to 103.1 on FM. Which has the longer wavelength, and by what factor is it larger?

Textbook Question

Radio-controlled clocks throughout the United States receive a radio signal from a transmitter in Fort Collins, Colorado, that accurately (within a microsecond) marks the beginning of each minute. A slight amount of time is added by a clock at any location to correct for the signal travel time to the clock from Fort Collins. Assuming Fort Collins is no more than 3000 km from any point in the U.S., what is the longest travel-time delay?

Textbook Question

The average intensity of a particular TV station’s signal is 1.0 x 10-13 W/m2 when it arrives at a 33-cm-diameter satellite TV antenna. (a) Calculate the total energy received by the antenna during 3.0 hours of viewing this station’s programs. (b) Estimate the amplitudes of the E and B fields of the EM wave.

Textbook Question

A satellite beams microwave radiation with a power of 16 kW toward the Earth’s surface, 550 km away. When the beam strikes Earth, its circular diameter is about 1500 m. Find the rms electric field strength of the beam.

Textbook Question

An amateur radio operator wishes to build a receiver that can tune a range from 14.0 MHz to 15.0 MHz. A variable capacitor has a minimum capacitance of 95 pF.

(a) What is the required value of the inductance?

(b) What is the maximum capacitance used on the variable capacitor?

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