Vibrations and Waves

 What is Vibration?

A vibration is a back-and-forth motion of an object around a fixed point or
A periodic disturbance or motion about a fixed position.
In simple terms, it is a repeated movement that happens over and over again. 

 Example:

• The movement of a pendulum.
• The strings of a guitar when plucked.
• The diaphragm of a speaker when it produces sound.
• a swing moving back and forth.

Properties of Vibration and Important Terms in Vibration

 

• One complete vibration (oscillation): when an object moves from the starting point, goes to the farthest point, returns, and repeats the same motion.
• Equilibrium Position:The point where the object experiences no net force.
• Amplitude:The maximum displacement of the object from its equilibrium position.
• Period:The time taken for one complete cycle of oscillation.
• Frequency:The number of oscillations per unit time.
• Restoring Force:The force that pulls the object back towards its equilibrium position.

Parameters of Vibration

• Amplitude (A):Maximum displacement of the vibrating object from its equilibrium position. (Unit: meter)
• Period (T):Time taken for one complete cycle of vibration. (Unit: second)
• Frequency (f):Number of vibrations per unit time. (Unit: Hertz (Hz)) 

 The Pendulum

A pendulum is a simple device that swings back and forth freely under the influence of gravity.
It usually consists of a weight (called a bob) attached to the end of a string or rod that is fixed at one point.

Examples of pendulums:

• The swinging pendulum in a wall clock.
• A swing in a playground.
• A science experiment using a small ball and string.

Parts of a Pendulum

 

 

1. Bob → the weight at the end of the string.

2. String or Rod → holds the bob and allows it to swing.

3. Fixed Point → the point where the string is attached, allowing the pendulum to move freely.

4. Equilibrium Position → the central position where the pendulum naturally rests.

 

How a Pendulum Works

When the pendulum is pulled to one side and released, it swings because of gravity.

• At the highest point, the pendulum has maximum potential energy.

• As it moves down, this energy changes into kinetic energy (energy of motion).

• At the lowest point, the pendulum has maximum speed.

• Then it moves up to the other side, repeating the motion.

This repeated motion is called a vibration or oscillation.

  Formula:

 

 

where


f = frequency (Hz)
T = period (s)
n = One complete vibration (oscillation)
t = time (s) 

 

 Exercises

Short Answer Questions 

1. What is meant by one complete vibration (oscillation)? 
2. What is the definition of frequency?
3. Write the formula for calculating frequency. 

Essay Questions 

1. Explain what a vibration is and give two real-life examples that show vibration in daily life.
2. Describe one complete vibration (oscillation). Use your own words and include a simple illustration if needed.
3. Explain the difference between period and frequency. How are they related to each other?
4. A pendulum is pulled to one side and released. Describe step-by-step what happens to the pendulum during one full vibration.
5.  A pendulum completes 40 vibrations in 20 seconds. Calculate the frequency and the period of the pendulum. Explain your steps clearly.

 

WAVES

A wave is a disturbance that transfers energy from one place to another without moving matter permanently.

Waves can travel through solids, liquids, gases, or even empty space (for certain types of waves).

Examples of waves:

• Water waves

• Sound waves

• Light waves

• Waves on a rope

 

Types of Waves

 

A. Based on the Direction of Vibration

1) Transverse Waves

• The vibration of particles is perpendicular (up and down) to the direction the wave travels.

• Has crests (highest points) and troughs (lowest points).

Examples:

• Waves on a rope

• Water waves

• Light waves

2) Longitudinal Waves

• The vibration of particles is parallel (back and forth) to the direction the wave travels.

• Has compressions (particles close together) and rarefactions (particles spread apart).

Example:

• Sound waves

Parts of a Wave

Transverse Wave Parts:

 

• Crest: highest point of a wave

• Trough: lowest point

• Wavelength (λ): distance between two crests or two troughs

• Amplitude: height of the wave from the middle to the crest or trough

   

Longitudinal Wave Parts:

 

• Compression: area where particles are close

• Rarefaction: area where particles are spread out

• Wavelength: distance between two compressions or two rarefactions

 

 

source : https://byjus.com/physics/difference-between-longitudinal-and-transverse-wave/ 

 

Wave Characteristics

1) Frequency (f)

• Number of waves or vibrations produced per second.

• Measured in Hertz (Hz).

2) Period (T)

• Time needed to complete one wave or one vibration.

• Measured in seconds (s).

Formula:

$$f = \frac{1}{T} \quad \text{and} \quad T = \frac{1}{f}$$

3) Wave Speed (v)

• The speed at which a wave travels.

Formula:

$$v=f\times \lambda$$

Where:
$v$ = wave speed (m/s)
$f$ = frequency (Hz)
$or lambda$ = wavelength (m)

 

B. Types of Waves Based on the Medium

Waves can be classified into two types based on whether they need a medium to travel:

 1. Mechanical Waves

Mechanical waves require a medium (such as air, water, or solids) to travel.

They cannot travel through a vacuum (empty space).

Examples:

• Sound waves
• Water waves
• Waves on a rope or spring
• Earthquake waves (seismic waves)

Particles of the medium vibrate to transfer energy. They can be transverse or longitudinal waves.

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2. Electromagnetic Waves

Electromagnetic waves do NOT need a medium. They can travel through empty space (vacuum).

Examples:

• Light

• Radio waves

• Microwaves

• X-rays

• Gamma rays

Made of oscillating electric and magnetic fields. All electromagnetic waves travel at the speed of light in a vacuum (≈ 3 × 10⁸ m/s). 

 Exercises

Essay Questions

1. A water wave has a frequency of 5 Hz and a wavelength of 0.8 meters. Calculate the speed of the wave and explain each step of your calculation. 
2. A rope wave travels with a speed of 12 m/s and its frequency is 3 Hz. Find the wavelength of the wave. Show your work clearly. 
3. A student creates waves in a spring. The waves move at 2 m/s, and one wave takes 0.25 seconds to pass a point. Calculate the frequency and wavelength of the wave. Write the formula and the steps. 
4. A wave completes 60 vibrations in 15 seconds. Calculate the frequency and the period of the wave. Explain how frequency and period are related.
5. 24 water waves pass a point in 6 seconds. What is the frequency of the waves? 
6.  How many wavelenght of this longitudinal picture below :

  

    7. The questions below refer to this diagram :

 

 

(a) Calculate the wavelength of the waves shown.

(b) What is the amplitude of these waves?

 

    8. A wave of wavelength 2 m travels 60 m in 12 seconds.

 

(a) What is the speed of the wave?

(b) How many waves would be produced in 12 seconds?

(c) What is the frequency of the wave?

  

9.  The questions below refer to this diagram : The waves travels in 5 seconds. Calculate the frequency and wavelength of the wave. Write the formula and the steps. 

 

 

10.