Understanding the Wavelength of Light and Sound Waves

The concept of wavelength is fundamental in understanding the behavior of waves, whether it be light or sound. This article delves into the calculation and significance of wavelengths, particularly for a light wave with a frequency of 4.3 x 1014 Hz and a sound wave with a frequency of 4.3 Hz. We will explore the formula and provide detailed calculations, ensuring a deep understanding of these concepts.

The Importance of the Speed of Light and Frequency

The speed of light in a vacuum is a constant value, denoted as c, and it is approximately 3.0 x 108 m/s. Frequency, on the other hand, is the number of oscillations or cycles per second, measured in Hertz (Hz). The relationship between these two is governed by the equation:

λ c / f

Calculating the Wavelength of Light with Frequency 4.3 x 1014 Hz

Given a frequency of 4.3 x 1014 Hz, we can calculate the wavelength of the corresponding light wave using the formula:

λ c / f (3.0 x 108 m/s) / (4.3 x 1014 Hz)

Calculation:

λ ≈ (3.0 x 108 m/s) / (4.3 x 1014 s-1) ≈ 6.98 x 10-7 m

Converting this to nanometers (nm), where 1 meter 109 nm:

λ ≈ 6.98 x 10-7 m x 109 nm/m 698 nm

This wavelength falls within the red region of the visible spectrum, which has a typical range of 620-750 nm. Technically, the Google reference is accurate: red light has a wavelength of approximately 700 nm, aligning with our calculated wavelength.

Wavelength of a Wave with a Frequency of 4.3 Hz

The speed of the wave is crucial when calculating the wavelength. The speed of light (c 3.0 x 108 m/s) is used for light, while different media (e.g., air, water, steel) influence the speed of sound waves dramatically.

For a sound wave with a frequency of 4.3 Hz in air, the relationship remains the same: V fλ. However, the speed of sound (V) in air depends on the medium's properties.

Using the given values:

V 4.3 m/s (hypothetical speed for simplicity)

f 4.3 Hz

λ V / f (4.3 m/s) / (4.3 Hz) 1 m

For a more accurate calculation, the speed of sound in air (approximately 343 m/s at room temperature) should be used. However, the conceptual approach remains valid.

Conclusion

Understanding and applying the formula λ c / f is essential for calculating the wavelength of both light and sound waves. Our detailed calculations for a light wave with a frequency of 4.3 x 1014 Hz resulted in a wavelength of approximately 698 nm, which falls within the red region of the visible spectrum. Similarly, understanding how the speed of the medium affects the wavelength of sound waves is crucial for broader applications in physics and engineering.