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Mastering Sound: Production, Transmission & Properties

CSEC Physics: The Science of Sound

Essential Understanding: Sound is a longitudinal mechanical wave that requires a medium to travel. Understanding how sound is produced, transmitted, and its properties is crucial for topics ranging from music to ultrasound technology. Master these fundamentals to excel in CSEC Physics.

🔑 Key Skill: Calculating Sound Speed (\(v = f\lambda\))
📈 Exam Focus: Longitudinal Wave Diagrams
🎯 Problem Solving: Echo Calculations & Ultrasound

The Nature of Sound Waves

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Production of Sound

Definition: Sound is produced by vibrating objects.

Mechanism:

  • Vibrating objects create pressure variations in the surrounding medium
  • These variations travel as longitudinal waves
  • Examples: Vocal cords, guitar strings, tuning forks
💡 Sound cannot travel through a vacuum – it needs a medium (solid, liquid, or gas)
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Transmission of Sound

How Sound Travels:

  1. Vibrating source causes air particles to vibrate
  2. Particles transfer energy to neighboring particles
  3. Wave travels through the medium as compressions and rarefactions

Speed in Different Media:

  • Solids (fastest): ~5000 m/s in steel
  • Liquids: ~1500 m/s in water
  • Gases (slowest): ~340 m/s in air
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Properties of Sound

Three Main Characteristics:

  1. Pitch: Determined by frequency (Hz)
  2. Loudness: Determined by amplitude
  3. Quality/Timbre: Determined by waveform

Human Hearing Range: 20 Hz to 20,000 Hz

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Sound as Longitudinal Waves

Key Feature: Particle vibration is parallel to wave direction

Compression
High pressure region
Particles close together
↔️
Rarefaction
Low pressure region
Particles far apart

Sound Wave Properties in Detail

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Pitch (Frequency)

Definition: How high or low a sound appears

Determined by: Frequency (Hz = vibrations/second)

  • High frequency = High pitch
  • Low frequency = Low pitch

CSEC Example: Middle C = 261.6 Hz, High C = 523.2 Hz

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Loudness (Amplitude)

Definition: How soft or loud a sound appears

Determined by: Amplitude of vibration

  • Large amplitude = Loud sound
  • Small amplitude = Soft sound

Measured in: Decibels (dB)

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Quality/Timbre

Definition: Characteristic that distinguishes different sounds of same pitch and loudness

Determined by: Waveform shape (harmonics/overtones)

Example: A violin and piano playing the same note sound different due to timbre

The Sound Wave Equation

The fundamental relationship connecting sound speed, frequency, and wavelength:

\[ v = f \lambda \]

Where:

  • \(v\) = speed of sound (m/s)
  • \(f\) = frequency (Hz)
  • \(\lambda\) = wavelength (m)
Speed of sound in air at room temperature: \(v \approx 340 \, \text{m/s}\)

Sound Wave Visualization

Longitudinal Sound Wave Diagram

Compression
High pressure
Rarefaction
Low pressure
Wavelength (λ)
Compression to compression
Amplitude
Pressure variation

Interactive Sound Wave Simulator

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Explore Sound Wave Properties

Objective: Adjust frequency and amplitude to see how they affect sound waves. Observe the oscilloscope display and pressure variations.

Low (Bass) ← → High (Treble)
Soft ← → Loud

Wavelength

0.77 m

Sound Speed (Air)

340 m/s

Wave Equation Check: \(v = f \times \lambda\) = 340 m/s

Note: Using speed of sound in air at 20°C = 340 m/s

Speed of Sound in Different Media

Medium Speed of Sound (m/s) Reason
Air (0°C) 331 Particles far apart, slow energy transfer
Air (20°C) 343 Warmer = faster particle movement
Water 1480 Particles closer together than in air
Steel 5000 Particles very close, strong bonds
Vacuum 0 No medium = no sound transmission
🔬 Key CSEC Fact: Speed of sound increases with temperature in gases. For every 1°C increase, speed increases by approximately 0.6 m/s.

Echoes & Ultrasound Applications

Echo Calculations

Echoes occur when sound reflects off surfaces. The time delay between the original sound and echo helps calculate distances.

\[ \text{Distance} = \frac{\text{Speed} \times \text{Time}}{2} \]
1
Example: A person claps hands and hears an echo after 2 seconds. Speed of sound is 340 m/s. How far away is the reflecting surface?
2
Solution: Sound travels to wall AND back, so total distance = 2 × distance to wall
3
Calculation:
Total distance traveled = speed × time = 340 × 2 = 680 m
Distance to wall = 680 ÷ 2 = 340 m
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Oscilloscope Display Simulator

Objective: See how different sounds appear on an oscilloscope. Compare waveforms of different instruments.

Oscilloscope Explanation: An oscilloscope displays voltage (vertical) vs. time (horizontal). For sound, it shows pressure variations over time.

Waveform Characteristics:

  • Sine Wave: Pure tone, single frequency (tuning fork)
  • Square Wave: Rich in odd harmonics (clarinet)
  • Sawtooth Wave: Rich in all harmonics (violin)
  • Complex Wave: Combination of frequencies (voice)

CSEC Worked Examples

1
Example 1: Calculating Wavelength
A sound wave has a frequency of 500 Hz. If the speed of sound in air is 340 m/s, calculate its wavelength.
Solution: Using \(v = f\lambda\) → \(\lambda = v/f = 340 / 500 = 0.68 \, \text{m}\)
2
Example 2: Echo Calculation
A ship uses sonar (sound navigation and ranging) to detect the sea floor. If the echo returns after 0.8 seconds and sound travels at 1500 m/s in seawater, how deep is the ocean at that point?
Solution: Sound travels down AND up, so total distance = speed × time = 1500 × 0.8 = 1200 m
Depth = 1200 ÷ 2 = 600 m
3
Example 3: Frequency & Pitch
A guitar string vibrates at 220 Hz. If the string is tightened to increase tension, will the pitch increase or decrease? Why?
Solution: The pitch will increase. Increasing tension increases the frequency of vibration. Higher frequency = higher pitch.
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CSEC Past Paper Question (2020)

Question: A student stands 85 m from a tall building and claps her hands. She hears an echo 0.5 seconds later.

(a) Calculate the speed of sound in air. [3 marks]

(b) If the temperature increases, what happens to the speed of sound? Explain. [2 marks]

(c) Why would she not hear an echo if she stood only 10 m from the building? [2 marks]

CSEC Practice Arena

Test Your Sound Knowledge

1
Which of the following is necessary for sound to travel?
Light
Heat
A medium
Electricity
Explanation: Sound is a mechanical wave that requires particles to vibrate. It cannot travel through a vacuum where there are no particles.
2
A sound wave has a frequency of 256 Hz and speed of 340 m/s. What is its wavelength?
0.75 m
1.33 m
2.56 m
87,040 m
Solution: Using \(v = f\lambda\) → \(\lambda = v/f = 340/256 = 1.33 \, \text{m}\)
3
Which property of sound would change if you pluck a guitar string harder?
Pitch
Loudness
Quality
Speed
Explanation: Plucking harder increases the amplitude of vibration, which increases loudness. Pitch depends on frequency (tightness and length of string), quality depends on the instrument’s characteristics.
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CSEC Examination Mastery Tip

Sound Wave Diagrams:

  • Longitudinal Waves: Draw compressions as close-together lines and rarefactions as far-apart lines.
  • Label Clearly: Always mark compressions (C), rarefactions (R), wavelength (λ), and direction of wave travel.
  • Oscilloscope Traces: Remember that an oscilloscope shows displacement (or pressure) vs. time, NOT the actual longitudinal wave.
  • Echo Calculations: Sound travels TWICE the distance (to object and back). Don’t forget to divide by 2!

Common Pitfall: Confusing electromagnetic waves (light, radio) with mechanical waves (sound). Sound needs a medium; light doesn’t.

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