Describe the production of sound by vibrating sources

3.4 Sound – Production of Sound by Vibrating Sources 🎵

What is Sound?

Sound is a mechanical wave that travels through a medium (usually air) by the vibration of particles. When a source vibrates, it pushes and pulls on the surrounding air molecules, creating a series of compressions and rarefactions that propagate as a wave.

How Vibrating Sources Produce Sound

  1. The source (e.g. a guitar string, a speaker cone or a drum head) starts to vibrate.

  2. The vibration displaces nearby air molecules, creating alternating regions of high and low pressure.

  3. These pressure variations travel through the air as a longitudinal wave until they reach our ears.

Think of a rubber band being stretched and released – the band’s motion pushes on the air around it, just like a vibrating string does.

Types of Vibrating Sources

SourceExampleFrequency Range (Hz)Typical Amplitude
StringGuitar string80–1000Small
Air columnFlute200–2000Medium
Vibrating membraneDrum head50–500Large
Speaker coneLoudspeaker20–20 000Variable
Human voiceSinging85–255Small–Medium

Key Equations

The fundamental relationships that describe sound waves are:

  • Speed of sound in air: \$v = 331 + 0.6T\$ where \$T\$ is temperature in °C.

  • Frequency of a vibrating string: \$f = \frac{1}{2L}\sqrt{\frac{T}{\mu}}\$ where \$L\$ is length, \$T\$ is tension, and \$\mu\$ is mass per unit length.

  • Frequency of a standing wave in an air column: \$f = \frac{nv}{2L}\$ where \$n\$ is the harmonic number.

  • Amplitude of a simple harmonic oscillator: \$A = \frac{F}{m\omega^2}\$ where \$F\$ is driving force, \$m\$ mass, and \$\omega\$ angular frequency.

  • Pressure amplitude of a sound wave: \$\Delta P = \rho v \omega A\$ where \$\rho\$ is air density.

  • Sound intensity: \$I = \frac{1}{2}\rho v \omega^2 A^2\$.

  • Decibel level: \$L = 20\log{10}\frac{P}{P0}\$ where \$P\$ is sound pressure and \$P_0 = 2\times10^{-5}\,\text{Pa}\$.

Exam Tips

Tip 1: When asked to calculate frequency, always check if the problem involves a string, air column or a vibrating membrane and use the appropriate formula.



Tip 2: Remember that amplitude is proportional to the displacement of the source. If a source vibrates with a larger amplitude, the resulting sound will be louder.



Tip 3: Use the temperature correction for the speed of sound: \$v = 331 + 0.6T\$. This is handy for problems involving different temperatures.



Tip 4: When comparing loudness, use the decibel formula \$L = 20\log{10}\frac{P}{P0}\$. A 10 dB increase means the intensity is ten times greater.



Tip 5: For questions about wave propagation, remember that sound travels as a longitudinal wave – the particles move parallel to the direction of travel.

Key Concepts Summary

• Sound is a pressure wave created by vibrating sources.

• The speed of sound depends on temperature: \$v = 331 + 0.6T\$.

• Frequency of a vibrating string: \$f = \frac{1}{2L}\sqrt{\frac{T}{\mu}}\$.

• Sound intensity increases with the square of amplitude.

• Loudness is measured in decibels: \$L = 20\log{10}\frac{P}{P0}\$.

• Different sources (strings, membranes, air columns) produce different frequency ranges.