WAVES

Wave motion is a fundamental concept in physics, describing the transfer of energy through a medium without the permanent displacement of the medium itself. This phenomenon is evident in various forms, from the ripples on a pond's surface to the transmission of light from the sun.

Types of Waves

Waves can be broadly categorized based on their nature and the medium through which they propagate:

1. Mechanical Waves: These require a medium (solid, liquid, or gas) to travel through. The particles of the medium oscillate around their equilibrium positions, facilitating the wave's propagation. Mechanical waves are further divided into:

• Transverse Waves: In these waves, particles of the medium move perpendicular to the direction of the wave's travel. A classic example is waves on a stretched string, where the displacement of the string is at right angles to the direction of the wave's movement. The highest points are called crests, and the lowest are troughs.

• Longitudinal Waves: Here, particles oscillate parallel to the wave's direction of travel. Sound waves in air are a prime example, where compressions (regions of high pressure) and rarefactions (regions of low pressure) move in the same direction as the wave. 

  
  
  
  
  
    
  
  

2. Electromagnetic Waves: Unlike mechanical waves, electromagnetic waves do not require a medium and can propagate through a vacuum. They consist of oscillating electric and magnetic fields perpendicular to each other and to the direction of propagation. Examples include light, radio waves, and X-rays.

Parameters of Wave Motion

Understanding wave motion involves several key parameters:

• Amplitude (A): The maximum displacement of particles from their equilibrium position. In transverse waves, it's the height of the crest or depth of the trough.

• Wavelength (λ): The distance between successive points in phase, such as crest to crest or compression to compression.

• Frequency (f): The number of complete wave cycles passing a point per unit time, measured in hertz (Hz).

• Period (T): The time taken for one complete cycle of the wave, with $T = \frac{1}{f}$.

• Wave Speed (v): The rate at which the wave propagates through the medium, given by $v = f \times λ$.

Illustrations

Transverse Wave:

Longitudinal Wave:

Worked Examples (JAMB Exam Style)

1. Question: A wave has a frequency of 50 Hz and a wavelength of 2 meters. Calculate its speed.

   Solution:

   Using the formula $v = f \times λ$:

   $v = 50 \, \text{Hz} \times 2 \, \text{m} = 100 \, \text{m/s}$

2. Question: The equation of a wave traveling along the positive x-direction is given by $y = 0.25 \times 10^{-3} \sin(500t - 0.025x)$. Determine the angular frequency of the wave motion.

   Solution:

   The general form of a wave equation is $y = A \sin(\omega t - kx)$, where $\omega$ is the angular frequency.

   Comparing with the given equation:

   $\omega = 500 \, \text{rad/s}$

3. Question: If a sound wave travels from a cold air region to a hot air region, what happens to its wavelength?

   Solution:

   The speed of sound increases with temperature. Since $v = f \times λ$ and frequency remains constant, an increase in speed results in an increase in wavelength.

4. Question: Which of the following is true of light and sound waves?

   A. They both transmit energy.

   B. They both need a medium for propagation.

   C. They are both transverse waves.

   D. Their velocities in air are equal.

   Solution:

   Option A is correct. Both light and sound waves transmit energy. However, light waves are electromagnetic and do not require a medium, while sound waves are mechanical and do.

5. Question: A wave on a string is described by $y(x, t) = 0.02 \sin(30t - 4x)$. Determine the wavelength of the wave.

   Solution:

   The wave number $k = 4 \, \text{m}^{-1}$.

   Wavelength $λ = \frac{2\pi}{k} = \frac{2\pi}{4} = 1.57 \, \text{m}$

Here are 10 JAMB exam practice questions based on the topic of wave motion, including mechanical and electromagnetic waves, and their parameters:

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Practice Questions

1. Question 1:
   A wave has a frequency of 20 Hz and a wavelength of 5 meters. What is the speed of the wave?
   A) 25 m/s
   B) 100 m/s
   C) 5 m/s
   D) 0.25 m/s

2. Question 2:
   Which of the following is a characteristic of electromagnetic waves?
   A) They require a medium to propagate
   B) They consist of oscillating electric and magnetic fields
   C) Their speed depends on the medium
   D) They are always longitudinal waves

3. Question 3:
   A transverse wave on a string has a maximum displacement of 0.05 m and a wavelength of 2 meters. What is the amplitude of the wave?
   A) 0.1 m
   B) 0.025 m
   C) 0.05 m
   D) 1 m

4. Question 4:
   A sound wave travels through air with a frequency of 500 Hz and a speed of 340 m/s. What is the wavelength of the sound wave?
   A) 0.68 m
   B) 1.0 m
   C) 0.68 cm
   D) 1.68 m

5. Question 5:
   Which of the following is true for longitudinal waves?
   A) The particles move perpendicular to the direction of wave propagation
   B) They involve compressions and rarefactions
   C) They cannot travel through solids
   D) They always travel at the speed of light

6. Question 6:
   The equation of a wave traveling along the x-axis is given by $y = 0.10 \sin(200t - 0.02x)$. What is the wave's angular frequency?
   A) 200 rad/s
   B) 100 rad/s
   C) 0.02 rad/s
   D) 0.10 rad/s

7. Question 7:
   A wave on a string has an amplitude of 0.05 m and a frequency of 50 Hz. If the speed of the wave is 10 m/s, what is the wavelength?
   A) 0.2 m
   B) 0.5 m
   C) 1.0 m
   D) 5.0 m

8. Question 8:
   Which of the following is true for mechanical waves?
   A) They can propagate through a vacuum
   B) They require a medium to propagate
   C) They only involve longitudinal waves
   D) They have no effect on the medium they travel through

9. Question 9:
   A sound wave has a frequency of 1,000 Hz and travels at a speed of 340 m/s. What is the period of the sound wave?
   A) 0.1 s
   B) 0.003 s
   C) 0.0029 s
   D) 0.03 s

10. Question 10:
    What happens to the speed of a mechanical wave as the temperature of the medium increases?
    A) It decreases
    B) It remains the same
    C) It increases
    D) It becomes zero

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Answers

1. Answer: B) 

2. Answer: B) 

3. Answer: C) 

4. Answer: A) 

5. Answer: B)

6. Answer: A) 

7. Answer: B) 

8. Answer: B) 

9. Answer: A)  

10. Answer: C) 
    

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These questions cover different aspects of wave motion, including wave speed, frequency, wavelength, types of waves, and characteristics of mechanical and electromagnetic waves.