Sound Wavelength Calculator

What is Sound Wavelength?

Sound wavelength is the distance between two consecutive compressions or rarefactions in a sound wave. It represents the spatial period of the wave—the distance over which the wave's shape repeats. Understanding wavelength is crucial in acoustics, as it relates to the pitch we perceive and how sound interacts with its environment.

Formula

The formula for calculating sound wavelength is:

\[ \lambda = \frac{v}{f} \]

Where:

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

Calculation Steps

Let's calculate the wavelength of a sound wave:

1. Given:
   • Speed of sound (\( v \)) = 343 m/s (in air at 20°C)
   • Frequency (\( f \)) = 440 Hz (A4 note)
2. Apply the wavelength formula: \[ \lambda = \frac{v}{f} \]
3. Substitute the known values: \[ \lambda = \frac{343 \text{ m/s}}{440 \text{ Hz}} \]
4. Perform the division: \[ \lambda \approx 0.78 \text{ m} \]

Example and Visual Representation

Let's visualize a sound wave and its wavelength:

This diagram illustrates:

• A sound wave represented by a sinusoidal curve (blue)
• The wavelength (\( \lambda \)) shown as the distance between two consecutive peaks (green)