Wave Motion: Types, Properties & Key Equations

What is a Wave?

A wave is a disturbance that travels through a medium (solid, liquid, or gas) or space, transferring energy without permanently displacing the medium.

Key Characteristics of Waves

1. Medium: The material through which a wave travels (e.g., water for water waves, air for sound waves).
2. Energy Transfer: Waves transfer energy, not matter.
3. Types of Waves:
   • Mechanical Waves: Need a medium (e.g., sound waves, water waves).
   • Electromagnetic Waves: Do not need a medium (e.g., light, radio waves).

Visual: Types of Waves

graph LR
    A["Waves"] --> B["Mechanical Waves"]
    A --> C["Electromagnetic Waves"]
    B --> D["Transverse Waves"]
    B --> E["Longitudinal Waves"]
    C --> F["Light Waves"]
    C --> G["Radio Waves"]

Types of Waves

1. Transverse Waves

• Definition: Particles of the medium move perpendicular to the direction of wave propagation.
• Examples: Water waves, light waves, waves on a string.
• Visual:

2. Longitudinal Waves

• Definition: Particles of the medium move parallel to the direction of wave propagation.
• Examples: Sound waves, seismic P-waves.
• Visual:

Comparison Table

Key Properties of Waves

1. Wavelength (λ)

• Distance between two consecutive crests or troughs (for transverse waves) or compressions (for longitudinal waves).
• Unit: Meter (m).

2. Frequency (f)

• Number of waves passing a point per second.
• Unit: Hertz (Hz) = 1/s.

3. Amplitude (A)

• Maximum displacement of particles from their equilibrium position.
• Unit: Meter (m).

4. Wave Speed (v)

• Speed at which the wave travels through the medium.
• Equation: $$v=f\times \lambda$$
• Unit: Meter per second (m/s).

Visual: Wave Properties

graph TD
    A["Wave"] --> B["Wavelength (λ)"]
    A --> C["Frequency (f)"]
    A --> D["Amplitude (A)"]
    A --> E["Wave Speed (v)"]
    E --> F["v = f × λ"]

Solved Example 1: Calculating Wave Speed

Problem: A wave has a frequency of 5 Hz and a wavelength of 2 m. Calculate its speed.

Solution: Given:

• $f=5\text{Hz}$
• $\lambda =2\text{m}$

Using the equation: $$v=f\times \lambda =5\times 2=10\text{m/s}$$

Answer: The wave speed is 10 m/s.

Solved Example 2: Calculating Frequency

Problem: A wave travels at 20 m/s with a wavelength of 4 m. Find its frequency.

Solution: Given:

• $v=20\text{m/s}$
• $\lambda =4\text{m}$

Rearranging the equation: $$f=\frac{v}{\lambda }=\frac{20}{4}=5\text{Hz}$$

Answer: The frequency is 5 Hz.

Wave Motion in Different Media

1. Wave Speed in a String

For a wave traveling along a stretched string: $$v=\sqrt{\frac{T}{\mu }}$$ where:

• $T$ = Tension in the string (N)
• $\mu$ = Linear mass density (kg/m)

2. Wave Speed in a Solid Rod

For a wave traveling along a solid rod: $$v=\sqrt{\frac{Y}{\rho }}$$ where:

• $Y$ = Young’s modulus (N/m²)
• $\rho$ = Density of the rod (kg/m³)

3. Wave Speed in a Gas (Sound Waves)

For sound waves in air: $$v=\sqrt{\frac{\gamma P}{\rho }}$$ where:

• $\gamma$ = Adiabatic index (ratio of specific heats)
• $P$ = Pressure (Pa)
• $\rho$ = Density of the gas (kg/m³)

Practical Applications of Wave Motion

1. Music and Sound: Musical instruments produce waves that travel through air to reach our ears.
2. Communication: Radio waves (electromagnetic waves) carry information over long distances.
3. Medical Imaging: Ultrasound waves (mechanical waves) are used in medical imaging (e.g., pregnancy scans).
4. Seismology: Studying seismic waves helps predict earthquakes.

NEB Board-Style Questions

Short Answer Questions

1. Define wavelength and frequency. How are they related to wave speed?
2. Differentiate between transverse and longitudinal waves with examples.
3. A wave has a speed of 340 m/s and a frequency of 170 Hz. Calculate its wavelength.

Long Answer Questions

1. Explain the factors affecting the speed of a wave in a stretched string. Derive the formula for wave speed in a string.
2. Describe the properties of waves with the help of diagrams. How do these properties differ in transverse and longitudinal waves?

Exam Tip

• Memorize the wave speed equation: $v=f\times \lambda$. It is frequently tested in NEB exams.
• Understand the difference between transverse and longitudinal waves: Always draw diagrams to visualize particle motion.
• Practice numerical problems: Most questions involve calculating wavelength, frequency, or wave speed.
• Know applications: Questions may ask about real-world uses of waves (e.g., sound, light, ultrasound).

End of Note