Standing Wave Frequency Calculation: Understanding Node and Antinode Distances

In wave physics, standing waves are a vital phenomenon often encountered in various applications, from acoustics to quantum mechanics. Understanding the relationships between different wave properties, such as nodes, antinodes, wavelengths, and frequency, is crucial for accurate analysis and application. This article delves into the calculation of frequency based on the given distance between a node and the next antinode in a standing wave.

Understanding Standing Waves

A standing wave is a wave that appears to remain in a fixed position. Unlike traveling waves, they do not transfer energy from one location to another. They are comprised of two sets of traveling waves that interfere with each other, creating points of maximum displacement (antinodes) and points of zero displacement (nodes).

Key Properties of Standing Waves

Node and Antinode Distances

One of the fundamental characteristics of standing waves is the distance between a node and the next antinode. This distance is always one-quarter of the wavelength (λ/4). This property is crucial for determining the wavelength when given the distance between a node and an antinode.

Wavelength Calculation

Given that the distance between a node and the antinode is 6 cm, we can calculate the wavelength (λ) as follows:

Distance between node and antinode λ/4

Therefore, if the distance is 6 cm, the wavelength can be calculated as:

λ 4 × Distance 4 × 6 cm 24 cm

Converting this distance from centimeters to meters:

λ 24 cm 0.24 m

Wave Speed and Frequency

In wave mechanics, the wave speed (v) is related to the frequency (f) and wavelength (λ) through the equation:

v fλ

Given the wave speed (v) is 4 m/s and the wavelength (λ) is 0.24 m, we can calculate the frequency as:

f v/λ

Substituting the given values:

f 4 m/s / 0.24 m 16.67 Hz

Therefore, the frequency of the wave is approximately 16.67 Hz.

Conclusion

In conclusion, understanding the properties of standing waves and the relationships between their components is essential for accurate wave analysis. By knowing the distance between a node and the antinode, researchers and engineers can calculate the wavelength and subsequently determine the frequency of a wave using basic wave properties.