transmission of sounds and speed of sound

Physics Notes: Transmission of Sound & Speed of Sound

1. Sound Waves

Definition

  • Sound is a mechanical wave.

  • Sound is a longitudinal wave.

  • It requires a medium (air, water, solids) to travel.

Longitudinal Waves

Particles vibrate parallel to the direction of wave motion.

Regions of a Sound Wave

  • Compression = particles crowded together; high pressure

  • Rarefaction = particles spread apart; low pressure

Sound waves are often called pressure waves because they create alternating high- and low-pressure regions.

2. Mechanical vs. Electromagnetic Waves

Mechanical Waves

Electromagnetic Waves

Need a medium

Do not need a medium

Sound waves

Light waves

Cannot travel through vacuum

Can travel through vacuum

Evidence

A ringing bell inside a vacuum jar can be seen vibrating but cannot be heard because sound cannot travel through a vacuum.

3. Production of Sound

Vibrating Bell

  1. Bell vibrates.

  2. Air particles are pushed and pulled.

  3. Compressions and rarefactions form.

  4. Sound waves travel through air.

Thunder

  • Creates powerful pressure waves.

  • Can make windows rattle or break.

4. Soundproofing

Recording studios use:

  • Double glass panels

  • Vacuum between the panes

Since sound cannot travel through a vacuum, noise transmission is reduced.

Musical Instruments

5. String Instruments

Acoustic Guitar

Important parts:

  • Strings

  • Bridge

  • Saddle

  • Soundboard

  • Sound hole

Process:

  1. Strings vibrate.

  2. Vibrations travel through bridge and saddle.

  3. Soundboard vibrates.

  4. Soundboard pushes more air.

  5. Louder sound emerges through sound hole.

Key idea:

  • Most sound comes from the vibrating body, not directly from the strings.

6. Wind Instruments

Examples:

  • Flute

  • Panpipe

Sound is produced by:

  • Vibrating columns of air

  • Formation of standing waves

Standing Waves

Necessary condition:

Two waves of equal frequency and amplitude travel in opposite directions.

7. Human Voice

Main structures:

  • Lungs

  • Vocal cords

  • Surrounding muscles

Higher Pitch

  • Vocal cords stretched

  • Greater tension

Lower Pitch

  • Vocal cords relaxed

  • Less tension

Speed of Sound

8. Speed of Sound vs. Light

Wave

Speed

Light

3.0 × 10⁸ m/s

Sound in air (20°C)

343 m/s

Light travels about 900,000 times faster than sound.

Example

During a storm:

  • You see lightning first.

  • You hear thunder later.

9. Echoes

An echo occurs when sound reflects from a surface and returns.

Distance Formula

d=vtd = vtd=vt

Example:

  • Echo time = 3.0 s

  • One-way time = 1.5 s

d=(343)(1.5)d = (343)(1.5)d=(343)(1.5)d=514.5 md = 514.5\ md=514.5 m

Approximately 500 m away.

10. Echolocation

Used by:

  • Bats

  • Dolphins

Process:

  1. Emit sound.

  2. Sound reflects from object.

  3. Return time is measured.

  4. Distance is calculated.

11. SONAR

SONAR = Sound Navigation And Ranging

Used by:

  • Submarines

  • Ships

  • Divers

Process:

  1. Send sound pulse ("ping").

  2. Pulse reflects off object.

  3. Receiver detects reflection.

  4. Distance calculated using sound speed.

Wave Equations

12. Speed Equation

General definition:

v=ΔdΔtv=\frac{\Delta d}{\Delta t}v=ΔtΔd​

Where:

  • vvv = speed (m/s)

  • Δd\Delta dΔd = distance

  • Δt\Delta tΔt = time

13. Universal Wave Equation

v=λfv=\lambda fv=λf

Where:

  • vvv = wave speed (m/s)

  • λ\lambdaλ = wavelength (m)

  • fff = frequency (Hz)

Rearranged Forms

λ=vf\lambda = \frac{v}{f}λ=fv​f=vλf = \frac{v}{\lambda}f=λv​

14. Example Problem

Given:

  • v=340 m/sv = 340\ m/sv=340 m/s

  • f=420 Hzf = 420\ Hzf=420 Hz

Find wavelength.

λ=340420\lambda = \frac{340}{420}λ=420340​λ=0.81 m\lambda = 0.81\ mλ=0.81 m

Answer: 0.81 meters

Temperature and Sound

15. Effect of Temperature

As temperature increases:

  • Molecules move faster.

  • Energy transfers faster.

  • Speed of sound increases.

As temperature decreases:

  • Molecules move slower.

  • Speed of sound decreases.

16. Speed of Sound Formula in Air

v=331+0.6Tv=331+0.6Tv=331+0.6T

Where:

  • vvv = speed of sound (m/s)

  • TTT = temperature (°C)

17. Example

Temperature = 10°C

v=331+0.6(10)v = 331 + 0.6(10)v=331+0.6(10)v=331+6v = 331 + 6v=331+6v=337 m/sv = 337\ m/sv=337 m/s

Answer: 337 m/s

Key Facts to Memorize

  • Sound is a mechanical, longitudinal wave.

  • Sound requires a medium.

  • Compression = high pressure.

  • Rarefaction = low pressure.

  • Sound cannot travel through a vacuum.

  • Standing waves require waves moving in opposite directions.

  • Speed of sound in air at 20°C ≈ 343 m/s.

  • Light travels much faster than sound.

  • Universal wave equation: v=λfv=\lambda fv=λf.

  • Speed of sound in air: v=331+0.6Tv=331+0.6Tv=331+0.6T.

  • Higher temperature → higher speed of sound.

  • SONAR and echolocation use reflected sound waves to determine distance.