Sound
Introduction
Hearing is the sense by which we detect vibrations in our surroundings. When an object vibrates it disturbs the medium (usually air) around it and creates a pulse that travels away from the source. If this pulse reaches the ear it can make the eardrum vibrate and produce the sensation of sound. When the source produces a continuous succession of pulses the disturbance travels as a wave. In gases, liquids and solids these disturbances are pressure waves made of alternating regions of compression (high pressure) and rarefaction (low pressure).
Sound waves
Sound waves are longitudinal pressure waves. The particles of the medium oscillate back and forth along the direction of wave propagation, creating compressions and rarefactions. Because these are pressure variations, the speed and transmission of sound depend on the medium's properties such as the particle spacing and temperature.
Tuning fork - an example of a sound source
A tuning fork produces sound when its prongs vibrate. As a prong moves outward it pushes nearby air particles together to form a compression; as it moves inward it creates a rarefaction. This alternating sequence of compressions and rarefactions propagates through the air as a sound wave. The frequency of the fork's vibration determines the pitch of the sound; the amplitude of vibration determines its loudness.
Activity: Build your own telephone
Materials:
- Two tin cans or two paper cups
- String
- Two toothpicks or small sticks
Procedure:
- Tie a toothpick on each end of a length of string.
- Make a small hole in the base of each can or cup. Push a toothpick through the hole so it rests on the inside bottom. Pull the string tight so the toothpick holds the string in place. There should be one can or cup at each end.
- Keep the string taut and speak into one can while someone listens at the other. The listener should be able to hear you.
- Try tying a third can and string to the middle of the first string to make a simple party line. Test whether everyone can hear each other.
Explanation: Sound waves normally travel through air, but they can also travel along stretched string more efficiently. The string must be tight so mechanical vibrations (longitudinal disturbances) are transmitted along it. The cup amplifies the sound at the ends by directing the pressure variations toward the ear.
Speed of sound
The speed of sound depends on the medium and its temperature. Typical facts:
- At sea level and around 21 °C, the speed of sound in air is approximately 344 m·s-1.
- Sound travels faster in liquids than in gases and faster in solids than in liquids. This is because particles are closer together in solids and liquids, allowing pressure disturbances to propagate more quickly.
- The speed of sound increases with temperature because particles move more rapidly and transmit disturbances faster.
| Substance | Speed v (m·s-1) |
|---|---|
| Aluminium | 6420 |
| Brick | 3650 |
| Copper | 4760 |
| Glass | 5100 |
| Gold | 3240 |
| Lead | 2160 |
| Sea water | 1531 |
| Air, 0 °C | 331 |
| Air, 20 °C | 343 |
Informal experiment: Measuring the speed of sound in air
Aim: Measure the speed of sound using a visible signal and a stopwatch.
Apparatus: A loud sound source that can be seen when produced (starter pistol, flag and loud buzzer, etc.), a stopwatch, a known distance between two observers.
Method and reasoning: Light travels much faster than sound, so when the source is at a distance you will see the action almost instantly but hear the sound after a time delay. If you measure the distance D between the source and observer and the time difference t between seeing and hearing the event, the speed of sound v is
v = D ÷ t
For better accuracy take several readings and use the average time.
Reflection of sound and echoes
When sound waves encounter a surface they are reflected. If reflections arrive at the observer sufficiently delayed relative to the direct sound, they are heard as distinct echoes. Large, hard, smooth surfaces (for example cliffs or empty halls) produce clear reflections and can create audible echoes. The reflection of sound is the basis for several practical techniques.
SONAR and depth measurement
SONAR (Sound Navigation And Ranging) uses the reflection of sound from the seabed to measure depth. A pulse is emitted and the time until the echo returns is measured. Knowing the speed of sound in sea water, the depth can be calculated because the pulse travels down and back up.
QUESTION
A ship sends a signal to the bottom of the ocean to determine the depth of the ocean. The speed of sound in sea water is 1450 m·s-1. If the signal is received 1.5 seconds later, how deep is the ocean at that point?
SOLUTION
Given the total travel time for the signal is 1.5 s and the speed in sea water is 1450 m·s-1. The measured time is for the travel down to the seabed and back, so the one-way time is half the total time: 1.5 s ÷ 2 = 0.75 s.
The one-way distance d equals speed × time: d = 1450 m·s-1 × 0.75 s = 1087.5 m.
Thus the depth at that point is 1087.5 m.
Echolocation
Certain animals such as bats and dolphins emit sounds and listen for the returning echoes to form a mental map of their surroundings; this biological use of reflected sound is called echolocation. The animal estimates distance and the shape of objects from the time delay and quality of the reflected sound.
Characteristics of a sound wave
Sound has several measurable characteristics that relate to our perception:
- Pitch - perceived highness or lowness of a sound; related to frequency. Higher frequency → higher pitch.
- Loudness - perceived intensity or volume; related to the amplitude of the pressure variation.
- Tone - the quality or timbre of a sound determined by the waveform and its harmonic content.
Pitch and frequency
Frequency is measured in hertz (Hz) and determines pitch. The typical audible range for humans is approximately 20 Hz to 20 000 Hz. Sounds below 20 Hz are called infrasound; sounds above 20 000 Hz are ultrasound.
| Species | Lower frequency (Hz) | Upper frequency (Hz) |
|---|---|---|
| Humans | 20 | 20 000 |
| Dogs | 50 | 45 000 |
| Cats | 45 | 85 000 |
| Bats | 20 | 120 000 |
| Dolphins | 0.25 | 200 000 |
| Elephants | 5 | 10 000 |
Activity: Range of wavelengths
Using the speed of sound in air (assume 344 m·s-1), you can calculate the wavelength λ corresponding to a frequency f by λ = v ÷ f. Use the frequency limits in the table above to compute the shortest and longest wavelengths heard by each species.
Loudness and amplitude
The amplitude of a sound wave determines how much energy the wave carries and how loud a sound appears to a listener. Human perception of loudness also depends on the ear's sensitivity to different frequencies. More energetic vibrations lead to larger amplitudes and louder sounds.
Practical investigations and equipment
Comparing instruments
The size and shape of a sound-producing instrument influence the frequencies and amplitudes it can produce. Suggested investigations:
- Compare vuvuzelas or horns of different lengths and diameters to observe changes in pitch and loudness.
- Tap tuning forks of different sizes and compare their pitches and durations.
- Use a function generator and speaker to produce controlled frequencies and amplitudes; measure the resulting waveform with a microphone and an oscilloscope.
Function generator and oscilloscope
A function (signal) generator produces electrical signals of variable frequency and amplitude that can drive a speaker. A microphone converts sound back into an electrical signal which can be displayed on an oscilloscope. The oscilloscope's vertical control sets the displayed amplitude scale and the horizontal (time) control sets the time per division so one can measure frequency and amplitude from the trace.
Note: The oscilloscope always displays a transverse trace (voltage vs time). This is a representation of pressure variation converted to an electrical signal and does not imply that sound is a transverse mechanical wave.
Intensity of sound and decibels
Intensity is the power transmitted per unit area and is related to amplitude. The decibel (dB) scale is a logarithmic scale commonly used to express sound intensity levels. Because of the logarithmic nature, an increase of 10 dB corresponds roughly to a perceived doubling of loudness in many listening conditions.
| Source | Intensity level (dB) | Approx. factor relative to hearing threshold |
|---|---|---|
| Rocket launch | 180 | 1018 |
| Jet plane (close) | 140 | 1014 |
| Threshold of pain | 120 | 1012 |
| Rock band | 110 | 1011 |
| Factory | 80 | 108 |
| City traffic | 70 | 107 |
| Normal conversation | 60 | 106 |
| Library | 40 | 104 |
| Whisper | 20 | 102 |
| Threshold of hearing | 0 | 1 |
Ultrasound
Ultrasound refers to sound with frequency above 20 kHz. Several animals can detect or produce ultrasound; humans cannot normally hear these frequencies. Ultrasound has many applications:
| Application | Lowest frequency (kHz) | Highest frequency (kHz) |
|---|---|---|
| Cleaning (e.g. jewellery) | 20 | 40 |
| Material testing for flaws | 50 | 500 |
| Welding of plastics | 15 | 40 |
| Tumour ablation | 250 | 2000 |
Medical imaging (ultrasonography) uses reflected ultrasound to form images of internal soft tissues. An ultrasound pulse is sent into the body; reflections from boundaries between tissues of different acoustic impedance are recorded and used to construct an image. Ultrasound is widely used in pregnancy scans, organ imaging and some therapeutic applications (e.g. physiotherapy or focused ultrasound treatments). Ultrasonic cleaners use cavitation produced by high-frequency waves in a liquid to remove contaminants from small objects.
The physics of hearing
The human ear has three main sections: outer ear, middle ear and inner ear.
- The outer ear (pinna and ear canal) collects and funnels sound to the eardrum.
- The middle ear contains three small bones - the malleus (hammer), incus (anvil) and stapes (stirrup) - that transmit vibrations from the eardrum to the inner ear and act as an impedance-matching system between air and the fluid-filled inner ear.
- The inner ear contains the cochlea, a fluid-filled spiral structure with sensory hair cells that convert mechanical vibrations into nerve impulses transmitted along the auditory nerve to the brain.
Certain sounds can damage hearing. Exposure to sound levels above about 80 dB for prolonged periods can cause hearing loss; very loud sounds (near or above the threshold of pain, ~120 dB) can cause immediate damage. Protective measures include earplugs, earmuffs, limiting exposure time and increasing distance from loud sources.
Safety and group activity
Discuss in small groups the importance of hearing protection for people working in noisy environments (for example construction workers using jackhammers, airport ground crews, or factory workers). Consider acceptable exposure times at various decibel levels and the types of protective equipment available. Prepare a short report describing recommended safety measures and why they matter.
Summary
- Sound waves are longitudinal pressure waves made of compressions and rarefactions.
- Frequency determines pitch; human hearing is roughly 20 Hz to 20 000 Hz. Below 20 Hz is infrasound; above 20 000 Hz is ultrasound.
- Amplitude determines loudness; intensity measures energy per unit area and is expressed in decibels (dB).
- Sound travels faster in solids than in liquids and faster in liquids than in gases. Speed increases with temperature.
- Reflected sound produces echoes; reflection is used in SONAR and echolocation.
- Ultrasound has many industrial and medical uses including imaging, cleaning and material testing.
- Hearing can be damaged by high-intensity sound; protection and exposure limits are important.
Physical quantities and units used in sound
| Quantity | Unit name | Unit symbol |
|---|---|---|
| Velocity (v) | metre per second | m·s-1 |
| Wavelength (λ) | metre | m |
| Amplitude (A) | metre | m |
| Period (T) | second | s |
| Frequency (f) | hertz | Hz (s-1) |
Exercises and practice
Exercise: Study the diagram of a musical note (waveform). Redraw the waveform for the following cases:
- A note with a higher pitch (increase frequency, wavelength decreases).
- A note that is louder (increase amplitude).
- A note that is softer (decrease amplitude).
Practical tasks: repeat the telephone experiment, measure speed of sound outdoors on different days to see the effect of temperature, or use a function generator and microphone to display waveforms on an oscilloscope and compare frequency and amplitude changes.
