Sound wave speed, frequency, and wavelength are fundamental properties of sound waves. The speed of sound is how fast the wave travels through a medium. Frequency is the number of wave cycles that pass a fixed point per second. Wavelength is the distance between two consecutive crests or troughs of a wave.

The relationship between sound wave speed, frequency, and wavelength is expressed by the following equation:

\[ v = f \lambda \]

Where:

- \(v\) is the speed of sound, typically measured in meters per second (m/s)
- \(f\) is the frequency, measured in Hertz (Hz)
- \(\lambda\) (lambda) is the wavelength, measured in meters (m)

Let's calculate the wavelength of a sound wave with a frequency of 440 Hz traveling at 343 m/s (speed of sound in air at 20°C):

- Identify the known values:
- Speed (\(v\)) = 343 m/s
- Frequency (\(f\)) = 440 Hz

- Rearrange the formula to solve for wavelength: \[ \lambda = \frac{v}{f} \]
- Substitute the known values: \[ \lambda = \frac{343 \text{ m/s}}{440 \text{ Hz}} \]
- Perform the calculation: \[ \lambda \approx 0.78 \text{ m} \]

Let's visualize the relationship between speed, frequency, and wavelength for our example sound wave:

This visual representation shows:

- The wavelength (\(\lambda\)) of approximately 0.78 meters
- The speed of sound (\(v\)) at 343 m/s
- The frequency (\(f\)) of 440 Hz, represented by the wave cycles

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