Sound Wavelength Frequency Speed Calculator

What is Sound Wave Speed, Frequency, and Wavelength?

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.

Formula

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)

Calculation Steps

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):

1. Identify the known values:
   • Speed (\(v\)) = 343 m/s
   • Frequency (\(f\)) = 440 Hz
2. Rearrange the formula to solve for wavelength: \[ \lambda = \frac{v}{f} \]
3. Substitute the known values: \[ \lambda = \frac{343 \text{ m/s}}{440 \text{ Hz}} \]
4. Perform the calculation: \[ \lambda \approx 0.78 \text{ m} \]

Example and Visual Representation

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