What are the wavelengths of electromagnetic wave and sound wave of same frequency 1.9-kHz? Speed of electromagnetic wave is 3x108 m/s, speed of sound wave is 357 m/s.
What are the wavelengths of electromagnetic wave and sound wave of same frequency 1.9-kHz? Speed of electromagnetic wave is 3x108 m/s, speed of sound wave is 357 m/s.
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)...
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![### Wavelengths of Electromagnetic and Sound Waves
In this educational module, we will explore the wavelengths of electromagnetic and sound waves that share a common frequency of 1.9 kHz. The speed of the electromagnetic wave is given as \(3 \times 10^8 \, \text{m/s}\), and the speed of the sound wave is \(357 \, \text{m/s}\).
#### Wavelength of Electromagnetic Wave, \(\lambda_1\)
\[ \lambda_1 = \, \_\_\_\_ \]
Units: km (kilometers)
#### Wavelength of Sound Wave, \(\lambda_2\)
\[ \lambda_2 = \, \_\_\_\_ \]
Units: cm (centimeters)
#### Speed of Electromagnetic Wave in a Medium with Dielectric Constant \(\kappa = 2\)
Given the permeability:
\[ \mu = \mu_r \mu_0 = 1.6 \times 10^{-3} \, \text{H/m} \]
Calculate the speed of the electromagnetic wave \(v\) in the medium:
\[ v = \, \_\_\_\_ \]
Units: m/s (meters per second)
### Detailed Instructions:
To solve these problems, you will need to use the following formulas:
1. **Wavelength of Electromagnetic Wave**:
\[ \lambda_1 = \frac{v_{\text{em}}}{f} \]
where:
- \( v_{\text{em}} = 3 \times 10^8 \, \text{m/s} \) (speed of the electromagnetic wave)
- \( f = 1.9 \times 10^3 \, \text{Hz} \) (frequency)
2. **Wavelength of Sound Wave**:
\[ \lambda_2 = \frac{v_{\text{sound}}}{f} \]
where:
- \( v_{\text{sound}} = 357 \, \text{m/s} \) (speed of the sound wave)
- \( f = 1.9 \times 10^3 \, \text{Hz} \) (frequency)
3. **Speed of Electromagnetic Wave in the Medium**:
\[ v = \frac{1}{\sqrt{\kappa \mu_r \mu_0}}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa90f48aa-fe1f-4446-8e54-ba82906f66bc%2F1221903a-7cdf-416b-a466-19d9e1abaea1%2Fztlpwcd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Wavelengths of Electromagnetic and Sound Waves
In this educational module, we will explore the wavelengths of electromagnetic and sound waves that share a common frequency of 1.9 kHz. The speed of the electromagnetic wave is given as \(3 \times 10^8 \, \text{m/s}\), and the speed of the sound wave is \(357 \, \text{m/s}\).
#### Wavelength of Electromagnetic Wave, \(\lambda_1\)
\[ \lambda_1 = \, \_\_\_\_ \]
Units: km (kilometers)
#### Wavelength of Sound Wave, \(\lambda_2\)
\[ \lambda_2 = \, \_\_\_\_ \]
Units: cm (centimeters)
#### Speed of Electromagnetic Wave in a Medium with Dielectric Constant \(\kappa = 2\)
Given the permeability:
\[ \mu = \mu_r \mu_0 = 1.6 \times 10^{-3} \, \text{H/m} \]
Calculate the speed of the electromagnetic wave \(v\) in the medium:
\[ v = \, \_\_\_\_ \]
Units: m/s (meters per second)
### Detailed Instructions:
To solve these problems, you will need to use the following formulas:
1. **Wavelength of Electromagnetic Wave**:
\[ \lambda_1 = \frac{v_{\text{em}}}{f} \]
where:
- \( v_{\text{em}} = 3 \times 10^8 \, \text{m/s} \) (speed of the electromagnetic wave)
- \( f = 1.9 \times 10^3 \, \text{Hz} \) (frequency)
2. **Wavelength of Sound Wave**:
\[ \lambda_2 = \frac{v_{\text{sound}}}{f} \]
where:
- \( v_{\text{sound}} = 357 \, \text{m/s} \) (speed of the sound wave)
- \( f = 1.9 \times 10^3 \, \text{Hz} \) (frequency)
3. **Speed of Electromagnetic Wave in the Medium**:
\[ v = \frac{1}{\sqrt{\kappa \mu_r \mu_0}}
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