Final answer:
To find the frequency of electromagnetic radiation with the same wavelength as a middle C sound wave, first calculate the wavelength using the speed of sound and the sound's frequency. Then use that wavelength with the speed of light to find the electromagnetic wave's frequency, which will be in the radio spectrum.
Step-by-step explanation:
The speed of sound in dry air at 20°C is 343 m/s, and the middle C on a piano has a frequency of 261 Hz. To find the wavelength (λ) of this sound wave, we use the formula λ = v/f, where v is the speed of sound and f is the frequency. Plugging in the values, we get λ = 343 m/s ÷ 261 Hz, which calculates to approximately 1.314 meters per wave.
Electromagnetic radiation, such as light, travels significantly faster than sound. The speed of light in a vacuum is approximately 3 x 108 m/s. Assuming the question asks for the frequency of electromagnetic radiation with the same wavelength as our sound wave, we again use the formula f = v/λ, with f now representing the frequency of the electromagnetic wave.
In this case, v is the speed of light, and λ is 1.314 meters. Therefore, the frequency is f = 3 x 108 m/s ÷ 1.314 meters, resulting in a frequency of approximately 2.28 x 108 Hz, which falls into the radio wave spectrum of the electromagnetic spectrum.