Question

The speed of sound in dry air at 20 ∘C is 343 m/s , and the middle C on a piano keyboard has a frequency of 261 Hz . λ = 1.31 m .What would be the frequency of electromagnetic radiation with the same wavelength?

Answer 1

The frequency of electromagnetic radiation with the same wavelength as the middle C sound wave (1.31 m) is approximately 2.29 x 10^8 Hz or 229 MHz.

Step-by-step explanation:

The frequency of electromagnetic radiation is determined by its speed divided by its wavelength. The speed of electromagnetic waves in a vacuum, which is the same for all wavelengths, is approximately 3 x 108 m/s.

Using the wavelength λ = 1.31 m given for the piano middle C (which pertains to sound waves in air), we can find the frequency of electromagnetic radiation of the same wavelength.

The frequency f of electromagnetic radiation is given by:
f = v / λ
where v is the speed of the electromagnetic wave and λ is the wavelength.

Substituting the values, we get:
f = (3 x 108 m/s) / 1.31 m
f ≈ 2.29 x 108 Hz or 229 MHz.