Question

Question #f8f9b

Answer 1

As frequency increases, the wavelength decreases by the same amount. It is an inverse relationship.

The relationship between frequency and wavelength is shown in the formula `v = f lambda`, where f is the frequency of the wave in Hz and `lambda` is the wavelength in m.

Let's take, for example, a sound wave at sea level when the temperature is `20^oC`. The speed of sound at this temperature is 343 m/s. (This can be calculated using the formula `v = 331 + 0.6T`.) Let's give this sound a frequency of 440 Hz.

Using this formula, solving for `lambda`, we have v/f = 343/440 = 0.780 m being the wavelength of this wave.

Let's now increase the frequency by an octave - to a frequency of 880 Hz. Now, solving for `lambda`, we have v/f = 343/880 = 0.390 m being the wavelength. By doubling the frequency, the wavelength was cut in half.