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Ch.6 - Electronic Structure of Atoms
Brown - Chemistry: The Central Science 14th Edition
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Tutti i libri di testoBrown 14th EditionCh.6 - Electronic Structure of AtomsProblema 1b
Capitolo 6, Problema 1b

The speed of sound in dry air at 20 °C is 343 m/s and the lowest frequency sound wave that the human ear can detect is approximately 20 Hz. (b) What would be the frequency of electromagnetic radiation with the same wavelength?

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Step 1: First, we need to find the wavelength of the sound wave. The speed of sound (v) is equal to the frequency (f) times the wavelength (λ). So, we can rearrange the equation v = fλ to solve for λ: λ = v/f. Substitute the given values into the equation: λ = 343 m/s / 20 Hz.
Step 2: Now, we have the wavelength of the sound wave. We can use this wavelength to find the frequency of the electromagnetic radiation. The speed of light (c) is equal to the frequency (f) times the wavelength (λ). So, we can rearrange the equation c = fλ to solve for f: f = c/λ.
Step 3: The speed of light (c) in a vacuum is approximately 3.00 x 10^8 m/s. Substitute this value and the wavelength we calculated in step 1 into the equation: f = 3.00 x 10^8 m/s / λ.
Step 4: The result will be the frequency of the electromagnetic radiation with the same wavelength as the sound wave. Remember that the frequency of electromagnetic radiation is usually expressed in hertz (Hz).
Step 5: Keep in mind that the frequency of electromagnetic radiation is much higher than that of sound waves because the speed of light is much greater than the speed of sound. This is why electromagnetic radiation can have the same wavelength as a sound wave but a much higher frequency.

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Wave Properties

Waves, including sound and electromagnetic waves, are characterized by their wavelength, frequency, and speed. The relationship between these properties is described by the equation: speed = frequency × wavelength. Understanding this relationship is crucial for solving problems involving different types of waves.
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Physical Properties

Electromagnetic Radiation

Electromagnetic radiation encompasses a range of waves, including visible light, radio waves, and X-rays, all of which travel at the speed of light in a vacuum. Unlike sound waves, which require a medium to propagate, electromagnetic waves can travel through a vacuum, making their behavior distinct and important in various applications, including communication and imaging.
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Electromagnetic Radiation Example

Frequency and Wavelength Conversion

To find the frequency of electromagnetic radiation with the same wavelength as a sound wave, one must first determine the wavelength of the sound wave using its speed and frequency. Once the wavelength is known, it can be used to calculate the frequency of the electromagnetic wave using the speed of light, demonstrating the interconnectedness of wave properties across different types of waves.
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Frequency-Wavelength Relationship
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Domanda del libro di testo

The speed of sound in dry air at 20 °C is 343 m/s and the lowest frequency sound wave that the human ear can detect is approximately 20 Hz. (a) What is the wavelength of such a sound wave?

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Domanda del libro di testo

A popular kitchen appliance produces electromagnetic radiation with a frequency of 2450 MHz. With reference to Figure 6.4, answer the following: (a) Estimate the wavelength of this radiation.

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Domanda del libro di testo

A popular kitchen appliance produces electromagnetic radiation with a frequency of 2450 MHz. With reference to Figure 6.4, answer the following: (c) If the radiation is not visible, do photons of this radiation have more or less energy than photons of visible light?

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Domanda del libro di testo

A popular kitchen appliance produces electromagnetic radiation with a frequency of 2450 MHz. With reference to Figure 6.4, answer the following: (b) Would the radiation produced by the appliance be visible to the human eye?

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