**Title: Understanding Radio Wave Intensity and Electric Field Amplitude****Introduction:**In this discussion, we examine the broadcast characteristics of an FM radio station and explore how to estimate the intensity of its broadcast waves and the electric field amplitude at a given distance.**Context:**FM radio station KETH in Los Angeles broadcasts on an assigned frequency of 101 MHz with a power of 50,000 watts.**Objectives:**1. **Estimate the Average Intensity of the Wave:** - Calculate the intensity at a distance of 59.5 kilometers from the radio antenna. - Assume the antenna radiates equally in all directions, meaning the intensity is constant over a hemisphere centered around the antenna.2. **Estimate the Amplitude of the Electric Field:** - Determine the amplitude of the electric field at this same distance.**Methodology:**- **Intensity Estimation:** Use the formula for intensity \( I = \frac{P}{A} \), where \( P \) is the power of the source and \( A \) is the area over which the power is spread. In this case, since the power spreads hemispherically, \( A \) can be calculated as half the surface area of a sphere (\( 2\pi r^2 \) where \( r = 59.5 \) km).- **Electric Field Amplitude:** Once the intensity is known, the amplitude of the electric field \( E \) can be calculated using \( E = \sqrt{2I \eta} \), where \( \eta \) is the impedance of free space (\(\approx 377 \, \Omega\)).By understanding these calculations, students can grasp the concepts of electromagnetic wave propagation in practical broadcasting scenarios.

Answered: Image /qna-images/answer/093801e7-6d7e-4db5-a47e-95040ab2d2ca.jpg

FM radio statIon KRTH in 1Urangeler pr1adiart on an assigned freguencey or lll MHZ a Lower Of 5O,000 W. (B ESHImate the average intensity Ot the wave at a distance oř 59.5 km) trom the raalo antenna. Assume tor the PUrpose Of this estimate tnal the antenia vadiates equally in ali directions, sI that the intensity Is constant over a hemisphere rentered on the antenna. OESHImate the amplitvde of the llectric Flela at this aIstance.

FM radio statIon KRTH in 1Urangeler pr1adiart on an assigned freguencey or lll MHZ a Lower Of 5O,000 W. (B ESHImate the average intensity Ot the wave at a distance oř 59.5 km) trom the raalo antenna. Assume tor the PUrpose Of this estimate tnal the antenia vadiates equally in ali directions, sI that the intensity Is constant over a hemisphere rentered on the antenna. OESHImate the amplitvde of the llectric Flela at this aIstance.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Related questions

Q: Bmvvbj

A: Approach to solving the question:Please see attached photos for detailed solutions. Thank you.…

Q: A mobile base station in an urban environment has a power measurement of 25 µW at 225 m. If the…

Q: A radio wave has a frequency of 25300H what is its wavelength

A: Given data: A radio wave Frequency (f) = 25300 Hz Required: Wavelength (λ)

Q: Check my work A police car is moving at 38.4 m/s to catch up with a speeder directly ahead. The…

Q: The sound waves travel with speed of 240 m/s. If is wavelength is 5 m. Find the frequency of wave ?

A: Given data : Speed of sound = v Wavelength =…

Q: a tissue has a wavelength of 0.50 mm. (a) What is the speed of sound, vs (in mm/µs) in this tissue?…

A: 1 M Hz = 106 Hz Wavelength = 0.5 mm = 0.5 × 10-3 m

Q: Needs Complete solution with 100 % accuracy don't use chat gpt or ai.

A: The objective of the question is to calculate the wavelength of the radio distress calls from ships…

Q: Light waves travel in a vacuum at a speed of 300,000 km/s. (a) The frequency of the longest visible…

A: Given values: Speed of light in vacuum, c=3×108 m/s The frequency of red light, fred=4×108 MHz…

Q: radio station broadcasts at a frequency of 600 kHz. Knowing that radio waves have a speed of 3 y…

Q: Equal loudness curves represent the results of measurements of A absolute threshold. B…

A: The equal loudness is often referred to as Fletcher Muson Curve. Which is related to physics and he…

Q: traveling with espeed of 3.50%, wave, has wavelength of 20 cm. Caleulate the freguency f this Uaue .

A: Given: Wave speed v=350 m/s, Wavelength λ=20 cm. Required: Frequency of the wave f. Wave speed is…

Concept explainers

Special Relativity

The theory of special relativity discusses how space and time are related to objects traveling along a straight line at a constant speed. Simply stated, as an object reaches the speed of light, its mass becomes infinite and it is unable to move faster than light. This interstellar speed limit has been the topic of much debate in astronomy, and also in science fiction when people consider how to fly over large distances.

Question

100%

**Title: Understanding Radio Wave Intensity and Electric Field Amplitude**

**Introduction:**

In this discussion, we examine the broadcast characteristics of an FM radio station and explore how to estimate the intensity of its broadcast waves and the electric field amplitude at a given distance.

**Context:**

FM radio station KETH in Los Angeles broadcasts on an assigned frequency of 101 MHz with a power of 50,000 watts.

**Objectives:**

1. **Estimate the Average Intensity of the Wave:**
- Calculate the intensity at a distance of 59.5 kilometers from the radio antenna.
- Assume the antenna radiates equally in all directions, meaning the intensity is constant over a hemisphere centered around the antenna.

2. **Estimate the Amplitude of the Electric Field:**
- Determine the amplitude of the electric field at this same distance.

**Methodology:**

- **Intensity Estimation:** Use the formula for intensity \( I = \frac{P}{A} \), where \( P \) is the power of the source and \( A \) is the area over which the power is spread. In this case, since the power spreads hemispherically, \( A \) can be calculated as half the surface area of a sphere (\( 2\pi r^2 \) where \( r = 59.5 \) km).

- **Electric Field Amplitude:** Once the intensity is known, the amplitude of the electric field \( E \) can be calculated using \( E = \sqrt{2I \eta} \), where \( \eta \) is the impedance of free space (\(\approx 377 \, \Omega\)).

By understanding these calculations, students can grasp the concepts of electromagnetic wave propagation in practical broadcasting scenarios.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

(a) To appreciate the human ear’s twelve order of magnitude (10^12) span from barely audible to the pain threshold, consider the following. Suppose an equivalently dynamic instrument were designed to measure distances. Taking the lower limit of the instrument to be 1.00 mm, what would be the largest distance measurable? (b) To provide a perspective for the human ear’s frequency sensitivity range (audible frequency extremes differ by 10^3 ), consider a speedometer with a similar speed range. If the speedometer’s maximum speed reading is 90.0 mi/h, what is the smallest finite speed that it could register?
What is the wavelenth of the waves from a radion station tht broadcasts at 107.1 MHZ?
(2) A 62 W (60 J/s) light bulb is 8.5% efficient, i.e. only 8.5% of the electrical energy it consumes (62 J each second) is converted to light and the rest is converted to waste heat. What is the light intensity 10 cm from the bulb in W/m2? (answer: 42 W/m?)
(II) One CD player is said to have a signal-to-noise ratioof 82 dB, whereas for a second CD player it is 98 dB. Whatis the ratio of intensities of the signal and the backgroundnoise for each device?
What wavelength EM wave would be emitted most strongly by matter at the temperature of the core of a nuclear explosion, about 13,500,000 K?mWhat type of wave is this?