Lesson Notes By Weeks and Term v5 - Grade 10

Lesson Video

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Performance objectives

• Define longitudinal waves and contrast them with transverse waves.
• Explain how sound is produced and travels through different media.
• Calculate the speed of sound.
• Define wavelength, frequency, period, and amplitude for sound waves.
• Relate frequency to pitch and amplitude to loudness.

Lesson summary

Sound is all around us, from the vibrant rhythms of Gqom music to the comforting crackle of a fire on a cold winter night in the Drakensberg. Understanding how sound works is not just about science; it's about understanding the world around us and how we perceive it. This week, we'll delve into the fascinating world of longitudinal waves and sound, exploring its properties and behaviour. Knowledge of sound principles helps in fields such as architecture (designing concert halls with good acoustics), medicine (ultrasound imaging), and even music production. In South Africa, with its rich musical heritage, understanding sound is especially relevant.

Lesson notes

2.1 Longitudinal Waves: A longitudinal wave is a wave in which the displacement of the medium is parallel to the direction of propagation of the wave. This is in contrast to transverse waves, where the displacement is perpendicular to the direction of propagation (like a wave on a rope). Sound waves are a prime example of longitudinal waves. Imagine pushing a slinky back and forth along its length. The coils bunch up (compressions) and spread out (rarefactions) along the slinky, and this disturbance travels along the slinky. This is analogous to how sound travels through air. 2.2 Production of Sound Waves: Sound is produced by vibrating objects. When an object vibrates, it causes the particles of the surrounding medium (usually air) to vibrate as well. These vibrating particles then collide with their neighbours, transferring the energy and causing them to vibrate. This process continues, creating a chain reaction that propagates the sound wave outwards from the source.

Compressions: Regions where the air particles are pushed closer together, resulting in a higher density and pressure.

Rarefactions: Regions where the air particles are spread further apart, resulting in a lower density and pressure. Consider a loudspeaker. The speaker cone vibrates back and forth, creating alternating regions of compression and rarefaction in the air. These pressure variations travel outwards as a sound wave. 2.3 Propagation of Sound Waves: Sound waves require a medium to travel through; they cannot travel through a vacuum. This is because the particles of the medium are needed to transmit the vibrations. The speed of sound varies depending on the medium and its temperature.

Solids: Sound travels fastest in solids because the particles are closely packed together, allowing vibrations to be transmitted quickly.

Liquids: Sound travels slower in liquids than in solids but faster than in gases.

Gases: Sound travels slowest in gases because the particles are the furthest apart. The speed of sound in air is approximately 343 m/s at 20°C. The speed of sound increases with temperature. A rough estimate is that the speed of sound in air increases by about 0.6 m/s for every 1°C increase in temperature. 2.4 Speed of Sound Calculation: The speed of sound (v) can be calculated using the following formula: v = fλ where: v is the speed of sound (m/s) f is the frequency (Hz) λ is the wavelength (m) 2.5 Wavelength, Frequency, Period, and Amplitude: Wavelength (λ): The distance between two successive compressions or rarefactions in a sound wave. It's a spatial measurement (measured in meters, m).

Frequency (f): The number of complete vibrations (cycles) per second. It is measured in Hertz (Hz). A higher frequency means more cycles per second, and a higher pitched sound.

Period (T): The time taken for one complete vibration.

It is the inverse of frequency: T = 1/f (measured in seconds, s).

Amplitude: The maximum displacement of a particle from its resting position. For sound waves, amplitude corresponds to the amount of compression and rarefaction. A larger amplitude means a louder sound. 2.6 Relationship between Frequency/Pitch and Amplitude/Loudness: Frequency and Pitch: Pitch is our perception of how "high" or "low" a sound is. Higher frequency sound waves are perceived as higher pitched, and lower frequency waves are perceived as lower pitched. For example, a high note played on a piano has a higher frequency than a low note.

Amplitude and Loudness: Loudness is our perception of the intensity of a sound. Higher amplitude sound waves are perceived as louder, and lower amplitude waves are perceived as quieter. Think of turning up the volume on a radio; you are increasing the amplitude of the sound waves produced by the speaker.

Worked example

Example 1: A tuning fork vibrates at a frequency of 440 Hz. If the speed of sound in air is 343 m/s, what is the wavelength of the sound wave produced by the tuning fork?

Solution:

Given:

f = 440 Hz

v = 343 m/s

Using the formula v = fλ, we can rearrange it to solve for wavelength: