Wavelength and Frequency in Different Media

View Assign Share Link Report

Wavelength and Frequency in Different Media

This lesson aligns with NGSS PS4.A

Introduction

Understanding the relationship between wavelength and frequency is essential in the study of waves. This relationship is particularly important when considering how waves propagate through different media, such as air, water, and solids. This article explores how wavelength and frequency interact, how they change in different media, and the underlying principles that govern these changes.

Interdependence of Wavelength and Frequency

The relationship expressed by v=fλreveals the interdependence of wavelength and frequency:

Increasing Frequency: If the frequency of a wave increases while the wave speed remains constant, the wavelength must decrease.
Decreasing Frequency: Conversely, if the frequency decreases and wave speed is constant, the wavelength increases.

The Effect of Medium on Wave Speed

The speed of a wave varies significantly depending on the medium through which it travels. Different media have distinct physical properties, such as density and elasticity, which affect wave propagation. Understanding how these factors influence wave speed is critical for predicting changes in wavelength and frequency.

Sound Waves: Sound is a mechanical wave that requires a medium (such as air, water, or solid materials) for propagation. The speed of sound varies depending on the medium: Air: In dry air at 20°C (68°F), the speed of sound is approximately 343 meters per second (m/s). Water: Sound travels faster in water, approximately 1,484 m/s, due to water’s higher density and elasticity. Solids: Sound travels fastest in solids, such as steel, where the speed can exceed 5,000 m/s.
The wave speed for sound in a medium can be expressed by the formula:

where E is the elasticity (or bulk modulus) of the medium, and ρ is its density. This equation highlights how the medium's physical properties directly influence wave speed.

3. Light Waves:

Unlike sound waves, light waves are electromagnetic waves that can propagate

through a vacuum as well as through different media. However, when light enters a medium such as glass or water, its speed decreases:

Water: Light travels at about

$2.25×10^8 m/s$ in water.

Glass: The speed of light in glass is around

$2.00×10^8 m/s$ .

The change in speed affects the wavelength of light as it transitions between media while keeping the frequency constant. The refractive index (n) of a medium is defined as:

n=c/v

where c is the speed of light in a vacuum, and v is the speed of light in the medium. A higher refractive index indicates a slower speed of light in that medium, resulting in a shorter wavelength.

Calculating Wavelength and Frequency in Different Media

To illustrate how wavelength and frequency change in various media, let's consider specific examples:

Example 1: Sound in Air

Consider a sound wave with a frequency of 440 Hz (the pitch of the musical note A). We can calculate its wavelength in air:

$V_(air$ = 343 m/s(speed of sound in air)

Using the wave speed formula:

This calculation shows that a sound wave of 440 Hz has a wavelength of approximately 0.78 meters in air.

Example 2: Light in Water

Now, let’s consider a light wave traveling in water with a frequency of

$5×10^14$ Hz. The speed of light in water is approximately

$2.25×10^8$ m/s. We can calculate the wavelength:

This indicates that a light wave with a frequency of

$5×10^14$ Hz has a wavelength of approximately 0.45 micrometers (µm) in water.

The Role of Temperature and Pressure

In addition to the medium itself, temperature and pressure can significantly impact wave speed, and consequently, the relationship between wavelength and frequency. For sound waves, increasing the temperature generally leads to a higher speed of sound in gases, which, in turn, alters both frequency and wavelength.

Effect of Temperature:

In gases, the speed of sound increases by approximately 0.6 m/s for each degree Celsius increase in temperature. Therefore, at higher temperatures, sound waves travel faster, leading to shorter wavelengths for a constant frequency.

Effect of Pressure:

For gases, changes in pressure have a minimal effect on the speed of sound at constant temperature. However, in liquids and solids, pressure changes can alter density and elasticity, which can affect wave speed and consequently the relationship between wavelength and frequency.

Conclusion

The speed of a wave varies significantly depending on the medium through which it travels.
Different media have distinct physical properties, such as density and elasticity, which affect wave propagation.
Sound is a mechanical wave that requires a medium (such as air, water, or solid materials) for propagation.
Unlike sound waves, light waves are electromagnetic waves that can propagate through a vacuum as well as through different media.

Related Worksheets: