4aSound Waves and Speed of Sound
Explore longitudinal waves, compressions and rarefactions, the speed of sound in different media, and the decibel scale.
Sound is everywhere — from music and speech to medical ultrasound and sonar. Understanding how sound waves work and how their speed and intensity are measured is essential for acoustics, engineering, and medicine.
Lesson Overview
Sound is a mechanical longitudinal wave — particles of the medium vibrate parallel to the direction of wave travel, creating alternating regions of compression (high pressure) and rarefaction (low pressure). Sound requires a medium and cannot travel through a vacuum. In air at 20 °C, sound travels at approximately 343 m/s; it travels faster in liquids and solids because the particles are more tightly packed. The pitch of a sound corresponds to its frequency, while loudness corresponds to amplitude. Sound intensity is measured in decibels using β = 10 log(I / I₀), where I₀ = 1 × 10⁻¹² W/m² is the threshold of human hearing.
Key Concepts
Longitudinal Wave
Particles vibrate parallel to the direction of wave propagation
Compression
Region of high pressure where particles are pushed together
Rarefaction
Region of low pressure where particles are spread apart
Speed of Sound
~343 m/s in air at 20 °C; faster in liquids and solids
Pitch
Perceived highness or lowness of sound — determined by frequency
Intensity (Decibels)
β = 10 log(I / I₀); every 10 dB increase = 10× intensity
A sound wave travels through air at 20 °C. If its frequency is 440 Hz, what is its wavelength?
The intensity of a sound is 1 × 10⁻⁶ W/m². What is its intensity level in decibels? (I₀ = 1 × 10⁻¹² W/m²)
A sound increases from 50 dB to 70 dB. By what factor does the intensity increase?
Why does sound travel faster in steel (≈5100 m/s) than in air (343 m/s)?
A bat emits a 50 kHz ultrasonic pulse. What is the wavelength in air at 20 °C?
A sound wave in air has a wavelength of 0.5 m. What is its frequency?
Hint: Use v = fλ and solve for f. The speed of sound in air is 343 m/s.
The intensity of a rock concert is 1 × 10⁻² W/m². Calculate the sound level in dB.
Hint: Apply β = 10 log(I / I₀) with I₀ = 10⁻¹² W/m².
Two sounds have intensities I₁ and I₂ = 1000 I₁. What is the difference in their decibel levels?
Hint: Find β₂ − β₁ = 10 log(I₂/I₁).
Explain why you cannot hear an explosion on the Moon even if it is very large.
Hint: Think about what sound requires to travel.
A high-pitched whistle and a low-pitched foghorn both have the same loudness. How do their frequencies and amplitudes compare?
Hint: Pitch relates to frequency; loudness relates to amplitude.
Key Vocabulary
Longitudinal Wave
A wave in which the medium's particles vibrate parallel to the direction of energy propagation.
Example: Sound waves in air are longitudinal — air molecules compress and expand along the direction the sound travels.
Compression
A region in a longitudinal wave where particles are pushed together, creating high pressure.
Example: When a speaker cone moves forward, it creates a compression in the air in front of it.
Rarefaction
A region in a longitudinal wave where particles are spread apart, creating low pressure.
Example: As the speaker cone pulls back, it creates a rarefaction behind the compression.
Intensity
The power of a wave per unit area, measured in W/m².
Example: A sound 1 m from a speaker has higher intensity than the same sound heard 10 m away.
Decibel (dB)
A logarithmic unit for sound intensity level: β = 10 log(I / I₀).
Example: Normal conversation is about 60 dB; a jet engine is about 140 dB.
Interactive Practice — 5 Questions
Sound is classified as which type of wave?
What is the approximate speed of sound in air at 20 °C?
A sound has intensity I = 10⁻⁸ W/m². What is its level in dB?
Which property of a sound wave determines its pitch?
In which medium does sound travel fastest?
Independent Practice
A sound wave in air has frequency 256 Hz. Calculate its wavelength (v = 343 m/s).
The intensity of a sound is 10⁻⁴ W/m². Find the sound level in decibels.
Explain the difference between a compression and a rarefaction in a sound wave.
A sound level increases from 30 dB to 60 dB. By what factor does the intensity change?
★ A submarine uses sonar: it emits a 20 kHz pulse and detects the echo 0.4 s later. If the speed of sound in seawater is 1500 m/s, how far away is the object? Show all work.
ChallengeCommon Mistakes
Thinking sound can travel through a vacuum like light can.
Sound is a mechanical wave and requires a medium (solid, liquid, or gas) to propagate.
Confusing pitch with loudness — saying a high-pitched sound is always louder.
Pitch depends on frequency; loudness depends on amplitude. They are independent properties.
Assuming a 20 dB increase means the sound is twice as intense.
The decibel scale is logarithmic: 10 dB = 10× intensity, 20 dB = 100× intensity.
Math Tips
For decibels: β = 10 log(I / I₀). Remember I₀ = 10⁻¹² W/m². Every +10 dB multiplies intensity by 10.
Use v = fλ for all wave calculations. In air at 20 °C, v = 343 m/s.