Table of Contents
Sound Waves and Their Characteristics
1. Introduction
Sound is a form of mechanical energy produced by vibrating objects and transmitted through a material medium as a mechanical wave.
When an object vibrates, it produces disturbances in the surrounding medium. These disturbances travel through air, liquids or solids and may be detected by the human ear or by suitable instruments.
Sound plays an essential role in communication, music, navigation, medicine, industrial measurement and environmental monitoring.
2. Nature of Sound Waves
Sound waves are mechanical waves because they require a material medium for propagation.
In air, sound generally travels as a longitudinal wave. Air particles oscillate back and forth parallel to the direction in which the sound wave travels.
The movement of particles produces alternating regions of high and low pressure.
2.1 Compressions
A compression is a region in which particles are crowded closer together, producing relatively high pressure and density.
2.2 Rarefactions
A rarefaction is a region in which particles are relatively far apart, producing lower pressure and density.
A sound wave consists of successive compressions and rarefactions travelling through the medium.
2.3 Sound Requires a Medium
Sound cannot travel through a vacuum because there are no particles to transmit mechanical vibrations.
This is why sound cannot travel through empty space in the same way that electromagnetic waves do.
Sound can travel through:
- Gases
- Liquids
- Solids
3. Production of Sound
Sound is produced when an object vibrates and transfers energy to the surrounding medium.
Examples include:
- Vocal cords vibrating during speech
- Strings vibrating in musical instruments
- A drum membrane vibrating when struck
- A loudspeaker diaphragm moving back and forth
- A bell vibrating after being struck
The vibrating source produces pressure variations that propagate through the medium.
4. Main Characteristics of Sound Waves
The main physical characteristics of sound waves include frequency, wavelength, amplitude, time period, velocity and intensity.
4.1 Frequency
Frequency is the number of complete sound-wave cycles passing a fixed point per second.
[
f=\frac{1}{T}
]
Its SI unit is hertz (Hz).
Frequency determines the perceived pitch of a sound, although pitch is also influenced by the complexity and context of the sound.
Higher frequency generally produces a higher-pitched sound, while lower frequency produces a lower-pitched sound.
4.2 Wavelength
Wavelength is the distance between two consecutive compressions or two consecutive rarefactions.
It is represented by (\lambda) and measured in metres.
The relationship between velocity, frequency and wavelength is:
[
v=f\lambda
]
4.3 Amplitude
Amplitude is the maximum displacement of a vibrating particle from its equilibrium position.
For sound waves, greater amplitude generally corresponds to greater sound intensity and perceived loudness, provided other conditions remain comparable.
Amplitude is not the same as frequency.
4.4 Time Period
The time period is the time required for one complete oscillation.
[
T=\frac{1}{f}
]
A high-frequency sound has a short time period, while a low-frequency sound has a longer time period.
4.5 Velocity
Sound velocity is the distance travelled by a sound wave per unit time.
It depends on:
- The nature of the medium
- Temperature
- Density and elasticity of the medium
- Other environmental conditions
4.6 Intensity
Sound intensity is the sound power transmitted per unit area perpendicular to the direction of propagation.
[
I=\frac{P}{A}
]
Where:
- (I) = sound intensity in W/m²
- (P) = sound power in watts
- (A) = area in square metres
For a point source radiating uniformly in all directions:
[
I=\frac{P}{4\pi r^2}
]
Where (r) is the distance from the source.
This inverse-square relationship applies under ideal free-field conditions.
5. Pitch, Loudness and Quality
These are three important perceptual characteristics of sound.
5.1 Pitch
Pitch is the subjective perception of how high or low a sound is.
It is primarily related to frequency.
Examples:
- A whistle usually produces a high-pitched sound.
- A bass drum produces a low-pitched sound.
Pitch is a perceptual property, whereas frequency is a measurable physical quantity.
5.2 Loudness
Loudness is the subjective perception of the strength of a sound.
It depends mainly on sound intensity but is also influenced by frequency, duration and the sensitivity of the human ear.
A louder sound generally has greater intensity.
Loudness should not be treated as identical to intensity.
5.3 Quality or Timbre
Timbre is the characteristic quality that allows listeners to distinguish between sounds produced by different sources, even when they have the same pitch and approximate loudness.
For example, a piano and a violin can play the same musical note but sound different because of their different harmonic content and waveform characteristics.
6. Audible, Infrasonic and Ultrasonic Sound
Sound is classified according to frequency.
6.1 Audible Sound
The approximate frequency range of human hearing is:
[
20\text{ Hz to }20,000\text{ Hz}
]
This range varies with age, individual hearing ability and environmental conditions.
6.2 Infrasonic Sound
Infrasound refers to sound waves with frequencies below approximately 20 Hz.
Sources include:
- Earthquakes
- Volcanic activity
- Large storms
- Certain industrial machinery
- Some animal communication systems
Elephants can use low-frequency sounds for long-distance communication.
6.3 Ultrasonic Sound
Ultrasound refers to sound waves with frequencies above approximately 20,000 Hz.
It is used in:
- Medical imaging
- Industrial testing
- SONAR-related technologies
- Cleaning equipment
- Distance and level measurement
Bats and dolphins use ultrasonic signals in biological navigation and communication.
7. Longitudinal and Transverse Nature of Sound
Sound waves in fluids, such as air and water, propagate as longitudinal waves because fluids do not support ordinary bulk shear-wave propagation.
In solids, sound can propagate as both:
- Longitudinal waves
- Transverse or shear waves
This distinction is important in earthquake science and material testing.
8. Waveform and Harmonics
A pure tone is associated with a single frequency.
Many natural and musical sounds are complex waves consisting of a fundamental frequency and additional frequency components called harmonics or overtones.
The fundamental frequency is the lowest frequency component of a periodic sound.
Harmonics are integer multiples of the fundamental frequency:
[
f_n=nf_1
]
Where:
- (f_1) = fundamental frequency
- (n) = harmonic number
- (f_n) = frequency of the nth harmonic
The relative strengths of harmonics contribute to the timbre of a sound.
9. Sound Pressure and Decibel Scale
Sound produces small pressure variations around the ambient atmospheric pressure.
Sound pressure level is expressed in decibels (dB).
The sound pressure level is:
[
L_p=20\log_{10}\left(\frac{p}{p_0}\right)
]
Where:
- (L_p) = sound pressure level in dB
- (p) = measured root-mean-square sound pressure
- (p_0) = reference sound pressure
For sound in air, the commonly used reference pressure is:
[
p_0=20\ \mu\text{Pa}
]
The decibel scale is logarithmic. An increase of 10 dB represents a tenfold increase in sound intensity.
For sound intensity level:
[
L_I=10\log_{10}\left(\frac{I}{I_0}\right)
]
Where the commonly used reference intensity in air is:
[
I_0=10^{-12}\text{ W/m}^2
]
10. Reflection, Refraction and Diffraction of Sound
Sound waves exhibit several wave behaviours.
10.1 Reflection
Reflection occurs when sound waves strike a surface and return into the original medium.
It is responsible for echoes and contributes to reverberation.
10.2 Refraction
Refraction occurs when sound changes direction because its speed changes across regions of different temperature or other atmospheric conditions.
For example, sound may travel farther under certain atmospheric temperature conditions.
10.3 Diffraction
Diffraction is the bending or spreading of waves around obstacles and through openings.
Sound can often be heard around corners because of diffraction.
Diffraction is especially noticeable when the dimensions of an opening or obstacle are comparable to the wavelength.
11. Doppler Effect in Sound
The Doppler effect is the apparent change in frequency of a wave due to relative motion between the source and the observer.
Examples include:
- An ambulance siren sounding higher as it approaches and lower as it moves away
- The change in sound from a passing train
- Motion measurement using Doppler ultrasound
For a stationary observer and a moving source, a simplified expression is:
[
f’=f\left(\frac{v}{v-v_s}\right)
]
for a source approaching the observer, where:
- (f’) = observed frequency
- (f) = emitted frequency
- (v) = speed of sound
- (v_s) = source speed towards the observer
The observed frequency increases when the source approaches.
12. Worked Numerical Examples
Example 1: Frequency and Wavelength
A sound wave travels at 340 m/s and has a frequency of 680 Hz. Calculate its wavelength.
[
\lambda=\frac{v}{f}
]
[
\lambda=\frac{340}{680}=0.5\text{ m}
]
Answer: The wavelength is 0.5 m.
Example 2: Time Period
A sound wave has a frequency of 500 Hz. Calculate its time period.
[
T=\frac{1}{f}
]
[
T=\frac{1}{500}=0.002\text{ s}
]
Answer: The time period is 0.002 seconds or 2 milliseconds.
Example 3: Sound Intensity
A sound source emits 12 W of power uniformly in all directions. Calculate the intensity at a distance of 2 m.
[
I=\frac{P}{4\pi r^2}
]
[
I=\frac{12}{4\pi(2)^2}
]
[
I=\frac{12}{16\pi}\approx0.239\text{ W/m}^2
]
Answer: Approximately 0.239 W/m².
Example 4: Sound Intensity Level
A sound has an intensity of (10^{-6}\text{ W/m}^2). Calculate its intensity level using (I_0=10^{-12}\text{ W/m}^2).
[
L_I=10\log_{10}\left(\frac{I}{I_0}\right)
]
[
L_I=10\log_{10}(10^6)
]
[
L_I=60\text{ dB}
]
Answer: 60 dB.
Example 5: Frequency from Time Period
A vibrating source completes one cycle in 0.004 seconds. Calculate its frequency.
[
f=\frac{1}{T}
]
[
f=\frac{1}{0.004}=250\text{ Hz}
]
Answer: 250 Hz.
13. Applications of Sound Waves
Sound waves have numerous applications:
- Human communication through speech and hearing.
- Music and musical instruments.
- Medical diagnosis and ultrasound imaging.
- SONAR and underwater navigation.
- Industrial testing and flaw detection.
- Acoustic engineering and building design.
- Animal communication and echolocation.
- Environmental noise monitoring.
- Doppler-based flow and motion measurement.
- Security systems and acoustic sensors.
14. Common Examination Distinctions
- Sound is a mechanical wave and requires a medium.
- Sound cannot travel through a vacuum.
- Sound in air is longitudinal.
- Frequency is associated with pitch.
- Amplitude is related to loudness and intensity.
- Timbre distinguishes sounds with similar pitch and loudness.
- Infrasound lies below approximately 20 Hz.
- Ultrasound lies above approximately 20 kHz.
- Decibel is a logarithmic unit.
- The Doppler effect involves an apparent frequency change due to relative motion.
36 Key Takeaways for Exams
- Sound is a form of mechanical energy produced by vibrating objects.
- Sound requires a material medium for propagation.
- Sound cannot travel through a vacuum.
- Sound in air is a longitudinal wave.
- Longitudinal sound waves contain compressions and rarefactions.
- A compression is a region of relatively high pressure and density.
- A rarefaction is a region of relatively low pressure and density.
- Sound can travel through gases, liquids and solids.
- Frequency is the number of complete cycles per second.
- The SI unit of frequency is hertz.
- Wavelength is the distance between successive compressions or rarefactions.
- Amplitude is the maximum displacement from equilibrium.
- Wave velocity is given by (v=f\lambda).
- Time period is the reciprocal of frequency.
- Sound intensity is power transmitted per unit area.
- For an ideal point source, intensity varies inversely with the square of distance.
- Pitch is primarily related to frequency.
- Higher frequency generally produces higher pitch.
- Loudness is a subjective perception of sound strength.
- Loudness is related to intensity but is not identical to it.
- Timbre distinguishes sounds produced by different sources.
- The approximate human audible range is 20 Hz to 20 kHz.
- Infrasound has frequencies below approximately 20 Hz.
- Ultrasound has frequencies above approximately 20 kHz.
- Harmonics are integer multiples of a fundamental frequency.
- Sound pressure level is expressed in decibels.
- The decibel scale is logarithmic.
- A 10 dB increase corresponds to a tenfold increase in intensity.
- Reflection of sound produces echoes and contributes to reverberation.
- Refraction occurs when sound speed changes across regions.
- Diffraction allows sound to spread around obstacles.
- The Doppler effect is an apparent frequency change due to relative motion.
- An approaching sound source generally produces a higher observed frequency.
- A receding sound source generally produces a lower observed frequency.
- Bats and dolphins use ultrasonic signals for echolocation.
- Sound waves are widely used in communication, medicine, industry and navigation.