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Wave Transmission Calculator

Analyze wave transmission between different media, transmission coefficients, and wavelength changes

Parameters

mⓘ
Hzⓘ
mⓘ
m/sⓘ
m/sⓘ
Show Trail

Controls

xⓘ

Calculated Values

Transmission Coefficient:
0.37;0.37;
Wavelength in Medium 2:
4.41;m4.41;m
Speed Ratio:
4.41;4.41;
Transmitted Amplitude:
0.37;m0.37;m
Reflection Coefficient:
0.63;0.63;

Examples

Example 1: Sound in Air to Water

Sound wave transmitting from air (340 m/s) to water (1500 m/s).

  • Transmission Coefficient: 0.430.43
  • Wavelength in Medium 2: 1.501.50
  • Speed Ratio: 4.414.41

Example 2: Light in Air to Glass

Light wave transmitting from air (3×10⁸ m/s) to glass (2×10⁸ m/s).

  • Transmission Coefficient: 0.800.80
  • Wavelength in Medium 2: 0.000.00
  • Speed Ratio: 0.670.67

Example 3: Seismic Wave

Seismic wave transmitting from rock (5000 m/s) to soil (1000 m/s).

  • Transmission Coefficient: 0.330.33
  • Wavelength in Medium 2: 100.00100.00
  • Speed Ratio: 0.200.20

Visualization

Wave Transmission

Wave transmission occurs when a wave passes from one medium to another with different properties. The behavior of the transmitted wave depends on the relative properties of the two media, particularly their wave speeds and impedances.

When a wave enters a new medium, its frequency remains constant (frequency is a property of the source), but its wavelength and speed change according to the relationship v = λf. The wavelength in the second medium is λ₂ = λ₁(v₂/v₁).

The transmission coefficient (T) determines the amplitude of the transmitted wave relative to the incident wave. For normal incidence, T = 2Z₁/(Z₁ + Z₂), where Z₁ and Z₂ are the impedances of the two media.

Energy conservation requires that the sum of reflected and transmitted energy equals the incident energy. The transmitted energy is proportional to the square of the transmission coefficient.

Wave transmission is fundamental to understanding phenomena such as sound propagation through different materials, light refraction, and signal transmission in communication systems.

Key Concepts

  • Transmission Coefficient: Ratio of transmitted to incident wave amplitude
  • Frequency Conservation: Wave frequency remains constant across media
  • Wavelength Change: Wavelength changes with wave speed in new medium
  • Speed Ratio: Relationship between wave speeds in different media
  • Energy Conservation: Total energy is conserved during transmission
  • Impedance Matching: Maximum transmission when impedances are equal
  • Normal Incidence: Wave incident perpendicular to boundary
  • Medium Properties: Density and elasticity affect wave speed

Real-World Applications

  • Acoustics: Sound transmission through walls and materials
  • Optics: Light transmission through lenses and prisms
  • Seismology: Earthquake wave transmission through Earth layers
  • Electronics: Signal transmission in transmission lines
  • Medical Imaging: Ultrasound transmission through tissues

Explore Further

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  • Wave Interference

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  • Standing Waves

    Analyze standing wave patterns, nodes, antinodes, and resonance frequencies.

  • Wave Reflection

    Calculate reflection coefficients, phase shifts, and energy transfer at boundaries.

  • Wave Diffraction

    Study single slit diffraction patterns and interference minima.

Physics Equations

Transmission Coefficient:
T=2Z1Z1+Z2T = \frac{2Z_1}{Z_1 + Z_2}
Wavelength Change:
λ2=λ1v2v1\lambda_2 = \lambda_1\frac{v_2}{v_1}
Speed Ratio:
v2v1=λ2λ1\frac{v_2}{v_1} = \frac{\lambda_2}{\lambda_1}
Transmitted Amplitude:
At=TAiA_t = TA_i
Energy Conservation:
R2+T2=1R^2 + T^2 = 1

Step-by-Step Solution

See how the main results are calculated.

1

Step 1: Calculate Speed Ratio

First, we calculate the ratio of wave speeds in the two media:

Equation:

v2v1=λ2λ1\frac{v_2}{v_1} = \frac{\lambda_2}{\lambda_1}

Calculation:

v2v1=1500340=4.412\frac{v_2}{v_1} = \frac{1500}{340} = 4.412

Explanation:

The speed ratio determines how the wavelength changes in the new medium.

2

Step 2: Calculate New Wavelength

The wavelength in the second medium is:

Equation:

λ2=λ1v2v1\lambda_2 = \lambda_1\frac{v_2}{v_1}

Calculation:

λ2=1.00×4.412=4.41 m\lambda_2 = 1.00 \times 4.412 = 4.41 \text{ m}

Explanation:

The wavelength changes proportionally with the wave speed while frequency remains constant.

3

Step 3: Calculate Transmission Coefficient

For normal incidence, the transmission coefficient is:

Equation:

T=2Z1Z1+Z2=21+v2v1T = \frac{2Z_1}{Z_1 + Z_2} = \frac{2}{1 + \frac{v_2}{v_1}}

Calculation:

T=21+4.412=0.370T = \frac{2}{1 + 4.412} = 0.370

Explanation:

The transmission coefficient determines the amplitude of the transmitted wave.

4

Step 4: Calculate Transmitted Amplitude

The amplitude of the transmitted wave is:

Equation:

At=TAiA_t = TA_i

Calculation:

At=0.370×1.000=0.3696 mA_t = 0.370 \times 1.000 = 0.3696 \text{ m}

Explanation:

The transmitted amplitude is the product of transmission coefficient and incident amplitude.

Frequently Asked Questions (FAQ)

What is the transmission coefficient?

The transmission coefficient (T) is the ratio of the amplitude of the transmitted wave to the amplitude of the incident wave. It determines how much of the wave energy passes through the boundary between two media.

Why does wavelength change when a wave enters a new medium?

The frequency of a wave is determined by the source and remains constant. Since v = λf, when the wave speed changes in a new medium, the wavelength must change proportionally to maintain the same frequency.

What is impedance matching?

Impedance matching occurs when the impedances of two media are equal (Z₁ = Z₂). In this case, the transmission coefficient is maximum (T = 1) and no reflection occurs, ensuring maximum energy transfer.

How does energy conservation apply to wave transmission?

Energy conservation requires that R² + T² = 1, where R is the reflection coefficient and T is the transmission coefficient. This ensures that the total energy of the incident wave equals the sum of reflected and transmitted wave energies.

What happens when a wave enters a medium with higher wave speed?

When a wave enters a medium with higher wave speed, the wavelength increases while the frequency remains constant. The transmission coefficient depends on the impedance ratio, not just the speed ratio.

Practice MCQs

  1. When a wave enters a new medium, which property remains constant?
  2. The transmission coefficient is maximum when:
  3. If v₂ > v₁, then λ₂:
  4. The energy conservation equation for wave transmission is:
  5. A wave with amplitude A has transmission coefficient T. The transmitted amplitude is:

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