The relationship between the wavelength (λ), frequency (f), and speed of sound (v) in a medium can be described by the formula:
v = λf
This equation states that the speed of sound is equal to the wavelength multiplied by the frequency. If the speed of sound is constant, any change in frequency will result in a corresponding change in wavelength.
To understand this relationship, let's consider an example. Suppose you have a sound wave with a frequency of 1000 Hz and a speed of sound in the medium of 340 m/s (typical speed in air). Using the formula, we can rearrange it to solve for wavelength:
λ = v / f λ = 340 m/s / 1000 Hz λ = 0.34 m
In this case, the wavelength of the sound wave is 0.34 meters.
Now, let's consider another example with a higher frequency. If the frequency increases to 2000 Hz while the speed of sound remains the same, we can calculate the new wavelength:
λ = 340 m/s / 2000 Hz λ = 0.17 m
As you can see, the wavelength decreases as the frequency increases. This inverse relationship is true for sound waves in any medium as long as the speed of sound remains constant. When the frequency of a sound wave increases, the wavelength becomes shorter, and when the frequency decreases, the wavelength becomes longer.