The speed of sound in dry air at is 343 m/s, and the middle C on a piano keyboard has a frequency of 261 Hz. b. What would be the frequency of electromagnetic radiation with the same wavelength?

검증된 단계별 안내

Identify the relationship between speed, frequency, and wavelength for sound waves: \( v = f \cdot \lambda \), where \( v \) is the speed of sound, \( f \) is the frequency, and \( \lambda \) is the wavelength.

Calculate the wavelength of the sound wave using the given speed of sound (343 m/s) and the frequency of middle C (261 Hz): \( \lambda = \frac{v}{f} \).

Recognize that electromagnetic radiation also follows the wave equation: \( c = f_{em} \cdot \lambda \), where \( c \) is the speed of light (approximately \( 3.00 \times 10^8 \) m/s), \( f_{em} \) is the frequency of the electromagnetic wave, and \( \lambda \) is the wavelength.

Use the wavelength calculated from the sound wave to find the frequency of the electromagnetic radiation: \( f_{em} = \frac{c}{\lambda} \).

Substitute the known values into the equation to solve for the frequency of the electromagnetic radiation.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Wave Speed

Wave speed is the distance traveled by a wave per unit time. In the context of sound, it is determined by the medium through which it travels, such as air. The speed of sound in dry air at room temperature is approximately 343 m/s, which is essential for calculating the wavelength of sound waves.

Frequency and Wavelength Relationship

The relationship between frequency (f) and wavelength (λ) of a wave is described by the equation v = fλ, where v is the wave speed. This means that the frequency of a wave is inversely proportional to its wavelength; as frequency increases, wavelength decreases, and vice versa. This principle applies to both sound and electromagnetic 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 (approximately 3 x 10^8 m/s). The frequency of electromagnetic radiation can be calculated using the same wave speed and wavelength relationship as sound, allowing for comparisons between different types of waves.