Sound Waves

From the ringing of temple bells in Pashupatinath to the sound of traditional Nepali music during Dashain, sound is an essential part of our lives. Sound is a longitudinal mechanical wave that requires a medium to travel.

Nature of Sound

Sound waves are produced by vibrating objects. These vibrations create compressions (high-pressure regions) and rarefactions (low-pressure regions) in the medium.

Sound needs a medium: It travels through solids, liquids, and gases but cannot travel through vacuum. That is why there is no sound in outer space.

Speed of Sound

The speed of sound depends on the medium:

• In air (at 20 C): approximately 343 m/s
• In water: approximately 1500 m/s
• In steel: approximately 5000 m/s

Speed increases: solid > liquid > gas (because molecules are closer in solids)

Effect of temperature: In air, v = 331 + 0.6T m/s (where T is in Celsius).

Characteristics of Sound

• Pitch: Related to frequency. Higher frequency means higher pitch.
• Loudness: Related to amplitude. Larger amplitude means louder sound.
• Quality (Timbre): Distinguishes sounds of the same pitch and loudness from different sources.

Audible range for humans: 20 Hz to 20,000 Hz. Below 20 Hz is infrasound; above 20,000 Hz is ultrasound.

Resonance

When an object is forced to vibrate at its natural frequency, the amplitude increases dramatically. This is resonance.

Example: Pushing a swing at its natural frequency makes it go higher and higher. Soldiers break step while crossing a bridge to avoid resonance that could destroy the structure.

Beats

When two sound waves of slightly different frequencies overlap, we hear a periodic variation in loudness called beats.

Beat frequency = |f1 - f2|

Worked Example: Two tuning forks produce frequencies of 256 Hz and 260 Hz. How many beats per second are heard?

Beat frequency = |260 - 256| = 4 beats per second

Doppler Effect (Introduction)

The Doppler effect is the change in observed frequency when a source or observer is moving.

• Source moving toward observer: frequency increases (higher pitch)
• Source moving away from observer: frequency decreases (lower pitch)

This is why an ambulance siren sounds higher pitched as it approaches and lower pitched as it moves away.

Key Takeaways

• Sound is a longitudinal wave that needs a medium
• Speed of sound: solid > liquid > gas
• Resonance occurs when forcing frequency equals natural frequency
• Beat frequency equals the difference between two frequencies
• Doppler effect causes apparent frequency change due to relative motion