Sound waves — properties and applications (KCSE Physics Form 2)

TL;DR

Sound waves are vibrations that travel through a medium, carrying energy but not matter. Their key properties include amplitude, frequency, wavelength, and speed, which determine how we perceive sound. These properties are crucial for understanding how sound behaves and its many practical uses.

1. The Mental Model

Imagine dropping a stone into still water; ripples spread out, but the water itself doesn't move with the ripples. Sound waves are similar: they're disturbances that travel through air (or other stuff), making particles vibrate back and forth, but the particles don't actually travel with the sound.

2. The Core Material

What is Sound?

Sound is a form of energy produced by vibrations. When something vibrates, it pushes on the particles next to it, which then push on the next particles, and so on. This creates a chain reaction of compressions (where particles are squashed together) and rarefactions (where particles are spread apart) that travels through a medium. This traveling disturbance is a sound wave.

How Sound Travels

Sound needs a medium (like air, water, or solids) to travel. It cannot travel through a vacuum (empty space) because there are no particles to vibrate. The speed of sound depends on the medium: it travels fastest in solids, slower in liquids, and slowest in gases. This is because particles are closer together in solids, allowing vibrations to pass on more quickly.

Properties of Sound Waves

1. Amplitude: This is the maximum displacement of particles from their resting position. It determines the loudness or intensity of the sound. A larger amplitude means a louder sound.
2. Frequency (f): This is the number of complete vibrations (or cycles) per second. It's measured in Hertz (Hz). Frequency determines the pitch of the sound. High frequency means high pitch (like a whistle), and low frequency means low pitch (like a drum).
3. Wavelength (λ): This is the distance between two consecutive compressions or two consecutive rarefactions. It's measured in metres (m).
4. Speed (v): This is how fast the sound wave travels through the medium. It's measured in metres per second (m/s).

These properties are related by the wave equation:
Speed (v) = Frequency (f) × Wavelength (λ)

Reflection of Sound (Echoes)

When a sound wave hits a hard surface, it bounces back. This bouncing back is called reflection. An echo is a reflected sound that you hear as a distinct sound separate from the original sound. For you to hear a distinct echo, the reflecting surface must be far enough away for the sound to travel there and back, taking at least 0.1 seconds.

Refraction of Sound

Refraction is the bending of sound waves as they pass from one medium to another, or through different conditions within the same medium (e.g., air at different temperatures). This happens because the speed of sound changes. For example, sound travels faster in warmer air than in cooler air, causing sound to bend.

Diffraction of Sound

Diffraction is the spreading out of sound waves as they pass through an opening or around an obstacle. This is why you can hear someone talking around a corner even if you can't see them. Longer wavelengths (lower frequencies) diffract more easily than shorter wavelengths (higher frequencies).

Applications of Sound Waves

graph TD
    A[Sound Wave Properties] --> B{Applications}

    B --> C[Medical Imaging]
    C --> C1[Ultrasound scans for babies]
    C --> C2[Breaking kidney stones (lithotripsy)]

    B --> D[Navigation & Ranging]
    D --> D1[SONAR (Sound Navigation And Ranging) for submarines/fish finding]
    D --> D2[Echolocation by bats/dolphins]

    B --> E[Industrial Uses]
    E --> E1[Non-destructive testing (checking for cracks in materials)]
    E --> E2[Cleaning delicate instruments]

    B --> F[Communication]
    F --> F1[Telephones]
    F --> F2[Loudspeakers]

    B --> G[Music & Entertainment]
    G --> G1[Musical instruments]
    G1 --> G1a[Resonance in instruments]
    G --> G2[Concert hall acoustics]

1. Ultrasound: These are sound waves with frequencies above the human hearing range (above 20,000 Hz).
   • Medical uses: Imaging unborn babies, diagnosing organ problems, breaking kidney stones.
   • Industrial uses: Detecting flaws in materials, cleaning delicate equipment.
2. SONAR (Sound Navigation And Ranging): Used by ships and submarines to detect objects underwater, measure ocean depth, and locate fish. It works by sending out sound pulses and measuring the time it takes for the echo to return.
3. Echolocation: Animals like bats and dolphins use sound waves to navigate and hunt in the dark or murky water. They emit sounds and interpret the echoes.
4. Acoustics: The study of how sound behaves in enclosed spaces. Important in designing concert halls and recording studios to ensure good sound quality and minimize unwanted echoes.

3. Worked Example

A ship uses SONAR to measure the depth of the sea. It sends out a sound pulse, and the echo returns after 0.8 seconds. If the speed of sound in seawater is 1500 m/s, calculate the depth of the sea.

Solution:

1. Understand the problem: The sound travels from the ship to the seabed and back to the ship. So, the total distance covered is twice the depth of the sea.
2. Identify given values:
   • Time taken for echo (t) = 0.8 s
   • Speed of sound in seawater (v) = 1500 m/s
3. Recall the formula: Distance = Speed × Time
4. Calculate total distance:
   Total distance = 1500 m/s × 0.8 s = 1200 m
5. Calculate the depth: Since the total distance is twice the depth,
   Depth = Total distance / 2
   Depth = 1200 m / 2 = 600 m

The depth of the sea is 600 metres.

4. Key Takeaways

• Sound is produced by vibrations and needs a medium to travel.
• The speed of sound is fastest in solids, then liquids, then gases.
• Amplitude determines loudness, while frequency determines pitch.
• The wave equation relates speed, frequency, and wavelength: v = f × λ.
• Reflection of sound causes echoes, which are used in SONAR and echolocation.
• Ultrasound has frequencies above human hearing and is used in medicine and industry.

Common mistakes to avoid:
- Confusing loudness (amplitude) with pitch (frequency).
- Forgetting that sound cannot travel in a vacuum.
- Not dividing the total distance by two when calculating depth from an echo time.
- Assuming sound travels at the same speed in all materials.

5. Now Try It

Imagine you are standing 340 meters away from a large cliff. You shout, and you hear an echo. If the speed of sound in air is 340 m/s, calculate the time it takes for you to hear the echo. What would happen to the echo if the air temperature increased significantly? Explain your answer.

What success looks like: You should be able to calculate the time for the echo and explain how temperature affects the speed of sound and thus the echo.