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?

Verified step by step guidance

1. 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.
2. 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.
3. 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.
4. 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).
5. 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.

Key Concepts

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.

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.

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.