Sound Waves and Hearing
Understanding longitudinal waves, frequency, pitch, and ultrasound applications
Longitudinal Waves in Action
From whispers to ultrasound scans
Sound is a longitudinal wave that travels through a medium by creating alternating regions of compression and rarefaction. Unlike light, sound cannot travel through a vacuum—it needs particles to vibrate and transfer energy from source to ear.
How Sound Travels
When a speaker cone vibrates, it pushes air molecules together (compressions) and pulls them apart (rarefactions). These pressure variations travel outward as a wave, with particles vibrating parallel to the direction of wave travel. The speed depends on the medium: approximately 340 m/s in air, 1500 m/s in water, and 5000 m/s in steel—faster in denser materials where particles are closer together.
Frequency, Pitch, and Loudness
Frequency (measured in Hertz) determines pitch—how high or low a sound seems. A 2000 Hz whistle sounds high-pitched; a 100 Hz bass drum sounds low. Amplitudedetermines loudness, measured in decibels (dB). The human hearing range spans 20 Hz to 20,000 Hz, though this decreases with age. Sounds above 85 dB can cause hearing damage with prolonged exposure.
Echoes and Ultrasound
Sound reflects off hard surfaces, creating echoes. This principle enablessonar (submarines), echolocation (bats), and ultrasound imaging(medical scans). Ultrasound uses frequencies above 20 kHz—safe, non-ionizing radiation that can penetrate the body and reflect off tissue boundaries. The formula d = vt/2 calculates distance from echo time.
Wave Properties:
Longitudinal Wave: Sound particles vibrate parallel to wave direction. Compressions are high-pressure regions (particles close together), rarefactions are low-pressure regions (particles spread apart).
Decibel (dB) Loudness Scale
0 dB
Threshold of hearing
30 dB
Whisper
60 dB
Normal conversation
70 dB
Vacuum cleaner
85 dB
Heavy traffic (damage risk)
100 dB
Motorcycle
110 dB
Rock concert
120 dB
Pain threshold
140 dB
Jet engine (permanent damage)
Key fact: Every +10 dB approximately doubles the perceived loudness.
Prolonged exposure above 85 dB can cause hearing damage. Always wear ear protection at concerts and when using loud machinery.
Example 1: Wavelength Calculation
A sound wave has frequency 256 Hz (middle C note). Calculate its wavelength in air (v = 340 m/s) and water (v = 1500 m/s).
In air: λ = v/f = 340/256 = 1.33 m
In water: λ = v/f = 1500/256 = 5.86 m
Same frequency, longer wavelength in faster medium.
Example 2: Echo Distance
A person shouts toward a cliff and hears the echo after 4 seconds. How far away is the cliff?
d = (v × t) / 2
d = (340 × 4) / 2
d = 1360 / 2 = 680 m
Divide by 2 because sound travels to cliff AND back.
Example 3: Medical Ultrasound
Ultrasound at 2 MHz is used for imaging. If the echo returns in 0.0001 s through tissue (v = 1500 m/s), what is the tissue depth?
d = (v × t) / 2
d = (1500 × 0.0001) / 2
d = 0.15 / 2 = 0.075 m = 7.5 cm
Safe because non-ionizing (unlike X-rays).
Example 4: Decibel Comparison
A concert measures 110 dB. Normal conversation is 60 dB. How many times louder does the concert seem?
Difference = 110 - 60 = 50 dB
Every 10 dB ≈ doubles loudness
50 dB = 5 doublings = 2⁵ = 32 times louder
110 dB causes hearing damage—wear ear protection!
Term
Longitudinal Wave
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