Understanding the Calculation of Wave Length Using Frequency

Understanding the physics of waves is crucial in numerous applications, from telecommunications to engineering. One key aspect is grasping the relationship between frequency, wavelength, and the velocity of the wave. This article will delve into how to calculate the wavelength of a wave given its frequency at 100 Hz.

Calculating the Wavelength

The formula for calculating the wavelength of a wave is straightforward:

In this case, we have a wave with a frequency of 100 Hz. The relationship between wavelength, frequency, and the velocity of the wave is given by the equation:

Formula: Wavelength Velocity / Frequency

Lets break it down step-by-step using the example of a 100 Hz wave in a medium traveling at a velocity of 3 x 10^8 meters per second (m/s):

Velocity 3 x 10^8 m/s Frequency 100 Hz

Wavelength Velocity / Frequency
Wavelength 3 x 10^8 m/s / 100 Hz
Wavelength 3 x 10^6 m

Expressing the wavelength in a more readable format:

Wavelength 3 x 10^3 m

Understanding Frequency and Its Importance

Frequency is a fundamental concept in wave physics. It represents the number of waves that pass a fixed point in a given amount of time. For example:

If the time it takes for a wave to pass a fixed point is 1/2 second, the frequency is 2 per second. If the time is 1/100 of an hour, the frequency is 100 per hour.

Typically, frequency is measured in Hertz (Hz), named after the 19th-century German physicist Heinrich Rudolf Hertz. One Hertz corresponds to one cycle per second. Thus, if a frequency is 100 Hz, it means that the time taken for one full wave or complete oscillation is 1/100th of a second:

T 1 / Frequency
T 0.01 s

Related Concepts and Applications

Understanding the relationship between frequency and wavelength finds application in various fields. Here are a few key applications:

Telecommunications: The frequency range used by different communication systems (like 5G and Wi-Fi) is determined based on wavelength and the speed of light. Medical Imaging: In technologies like MRI and X-rays, the wavelength of energy waves is crucial for the imaging process. Audio Engineering: The frequency of sound waves determines the pitch of the sound, which is vital in music production and audio engineering.

Conclusion

Mastering the concept of frequency and wavelength is essential in many scientific and technological fields. Whether it's for designing communication systems, improving medical imaging technologies, or enhancing audio quality, a deep understanding of these concepts is indispensable.

Further Reading

For more information on the concepts discussed, refer to the following:

What is Frequency? Wavelength and Frequency in Physics