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Wavelength is an important characteristic of sound waves. It refers to the distance between successive crests or troughs, specifically, how far apart the wave fronts of the sound are from each other. To calculate wavelength, we use a simple formula:

• \(\lambda = \frac{v}{f}\)

Here, \(\lambda\) represents the wavelength in meters, \(v\) is the speed of sound in the medium (in meters per second), and \(f\) is the frequency of the sound wave in Hertz.
For example, if a sound wave in air has a speed of \(343 \, \text{m/s}\), which is typical at room temperature, and a frequency of \(425 \, \text{Hz}\), the wavelength would be calculated as follows:

• Substitute the known values: \(\lambda = \frac{343 \, \text{m/s}}{425 \, \text{Hz}}\).
• The result is approximately \(0.807 \, \text{meters}\).

This gives us an understanding of how frequent waves are spaced out in this given frequency.

The speed of sound is crucial in understanding sound wave behavior. It is the rate at which sound waves propagate through a medium. Sound travels at different speeds depending on the medium -- air, water, or solids are common mediums. At room temperature, the speed of sound in air is approximately \(343 \, \text{m/s}\).
Several factors influence the speed of sound:

• Medium: Sound travels faster in water and even faster in solids than in air.
• Temperature: Generally, the speed increases with higher temperatures in a given medium.
• Pressure li>Density of the medium.

Understanding the speed of sound helps in determining other properties such as wavelength if frequency is known, or frequency if wavelength is known, using their relationship with speed.

The relationship between frequency and wavelength is inverse and fundamental to wave physics. The formula \(\lambda = \frac{v}{f}\) highlights this. If the speed of sound \(v\) is constant, as it generally is in a given medium and conditions, changes in frequency \(f\) lead to opposite changes in wavelength \(\lambda\).

• If frequency increases, wavelength decreases.
• If frequency decreases, wavelength increases.

This concept explains why different frequencies result in different perceptions of sound, like pitch.
For example, increasing the frequency from \(425 \, \text{Hz}\) to \(475 \, \text{Hz}\) results in a wavelength change from approximately \(0.807 \, \text{m}\) to \(0.722 \, \text{m}\). The decrease in wavelength corresponds with the increase in frequency, illustrating their inversely proportional relationship.