Lesson Notes By Weeks and Term v5 - Grade 11

Lesson Video

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Performance objectives

• Waves are a fundamental part of our everyday lives, even if we don't always realize it. From the radio waves that bring us music and news to the light waves that allow us to see, and the sound waves we use for communication, waves play a crucial role. Understanding how waves behave, particularly the phenomenon of diffraction, is essential for designing technologies that improve communication, medical imaging, and even construction. In South Africa, where access to technology and infrastructure varies significantly, a strong understanding of wave properties can help us develop innovative and cost-effective solutions for various challenges. For instance, diffraction principles are critical in optimising cellphone tower placement to improve network coverage, especially in rural areas with uneven terrain.
• This week, we will focus on diffraction of waves, specifically 2D and 3D wavefronts. Diffraction is the bending of waves around obstacles or through openings. We will explore how the size of the opening or obstacle relative to the wavelength of the wave influences the amount of diffraction observed.
• By the end of this week, you will be able to:
• Objective 1: Define diffraction and explain its relationship to wavelength and obstacle/opening size.
• Objective 2: Sketch and interpret diagrams showing the diffraction of 2D water waves through single and double slits.

Lesson summary

Waves are a fundamental part of our everyday lives, even if we don't always realize it. From the radio waves that bring us music and news to the light waves that allow us to see, and the sound waves we use for communication, waves play a crucial role. Understanding how waves behave, particularly the phenomenon of diffraction, is essential for designing technologies that improve communication, medical imaging, and even construction. In South Africa, where access to technology and infrastructure varies significantly, a strong understanding of wave properties can help us develop innovative and cost-effective solutions for various challenges.

Lesson notes

What is Diffraction? Diffraction is the spreading of waves when they pass through an opening or around an obstacle. Unlike reflection and refraction, diffraction doesn't require a change in medium. It's purely a wave phenomenon caused by the superposition (interference) of waves emanating from different points on the wavefront as it passes the obstacle or opening.

Huygens' Principle: A crucial concept to understand diffraction is Huygens' Principle. This principle states that every point on a wavefront can be considered as a source of secondary spherical wavelets. The envelope (tangent) of these wavelets at a later time constitutes the new wavefront. This principle elegantly explains how waves propagate and, more importantly, how they bend around obstacles.

Diffraction and Wavelength: The amount of diffraction depends on the relationship between the wavelength (λ) of the wave and the size (d) of the opening or obstacle. λ > d (Wavelength much larger than the opening/obstacle): The wave essentially behaves as if the opening/obstacle isn't there. It diffracts almost spherically. 2D Wavefronts (Water Waves): Consider water waves passing through a narrow opening in a barrier. If the wavelength of the water waves is comparable to the width of the opening, the waves will spread out significantly on the other side of the barrier, creating circular wavefronts. This is readily observed in ripple tanks. Visualizing the superposition of wavelets from Huygens' principle is critical to understanding this.

Single Slit Diffraction: When a wave passes through a single slit, the spreading pattern is directly related to the ratio λ/d. A larger λ/d results in greater spreading.

Double Slit Diffraction: While usually associated with interference, double-slit experiments also demonstrate diffraction. The interference pattern is superimposed on the overall diffraction pattern. Each slit diffracts the wave, and the resulting waves then interfere with each other, creating a series of bright and dark fringes. 3D Wavefronts (Sound Waves): Sound waves are longitudinal waves and can diffract around corners and obstacles. This is why you can hear someone talking even if they are around a corner. The longer the wavelength of the sound (lower frequency), the more it diffracts. This is why you can often hear the bass from a distant sound system more clearly than the higher frequencies. Imagine you are walking in a stadium during a soccer match. People are chanting and singing. Sound from the people on the other side of the stadium (behind an obstacle like the roof support) can still reach you because it diffracts around the support. The lower the frequency of the chant, the more readily you hear it.

Diffraction of Light: Although light has a much smaller wavelength than sound, it can also be diffracted. Diffraction of light is more noticeable when light passes through very narrow openings or around very small obstacles. This phenomenon is crucial in understanding the resolving power of optical instruments like microscopes and telescopes. The finer the details you need to see, the more diffraction becomes a limiting factor.

Example 1: Water Waves in a Ripple Tank A ripple tank is set up with a barrier containing a single slit of width 5 cm. Water waves of wavelength 2 cm are generated. Describe what happens to the waves as they pass through the slit.

Solution: Since the wavelength (2 cm) is smaller than the slit width (5 cm), but not much smaller, diffraction will occur, but it won't be a completely circular wavefront emanating from the slit. The waves will spread out somewhat, but you will still see some "shadow" effect where the waves are less intense on either side of the direct path through the slit. The waves will bend around the edges of the slit opening.

Example 2: Sound Waves Around a Building A sound wave with a frequency of 100 Hz is produced. The wavelength of the sound wave is approximately 3.4 meters (using v = fλ, and v ≈ 340 m/s for the speed of sound in air). The sound encounters a building that is 10 meters wide. Will significant diffraction occur?

Solution: Since the wavelength (3.4 m) is smaller than the building width (10 m), but not negligibly so, some diffraction will occur. The sound will bend around the edges of the building, but there will be a significant "sound shadow" directly behind the building. Someone positioned directly behind the building will hear the sound, but it will be noticeably quieter than someone not blocked by the building.

Example 3: Radio Waves and a Hill A radio station transmits radio waves with a wavelength of 100 meters. The radio waves encounter a hill that is 50 meters wide. Will significant diffraction occur?

Solution: Since the wavelength (100 m) is larger than the width of the hill (50 m), significant diffraction will occur. The radio waves will bend significantly around the hill, allowing people on the other side of the hill to receive the radio signal.