Physics Learning Guide
Waves and Sound
Waves transfer energy from one place to another. Sound is a familiar type of wave produced by vibrations. Understanding waves and sound helps explain music, hearing, communication, earthquakes, medical ultrasound, musical instruments, and many engineering systems.
What Is a Wave?
A wave is a disturbance that travels through a medium or through space and transfers energy. In many mechanical waves, the particles of the medium vibrate around their equilibrium positions while the wave disturbance moves forward.
For example, when a water wave passes, the water does not travel forward with the wave over a long distance. Instead, the water particles mainly move up and down while energy moves across the surface.
Mechanical Waves
Mechanical waves require a material medium, such as air, water, a rope, or a solid. Sound waves are mechanical waves.
Electromagnetic Waves
Electromagnetic waves do not require a material medium. Light and radio waves can travel through the vacuum of space.
Important Wave Terms
Amplitude
Amplitude is the maximum displacement of a vibrating particle from its equilibrium position. A greater amplitude generally means that the wave transfers more energy.
Wavelength
Wavelength, represented by λ (lambda), is the distance between two adjacent points in the same phase of a wave. For example, it may be the distance from crest to crest, trough to trough, or compression to compression.
SI unit: metre (m).
Frequency
Frequency, represented by f, is the number of complete wave cycles passing a point each second.
SI unit: hertz (Hz), where 1 Hz means one cycle per second.
Period
Period, represented by T, is the time taken for one complete wave cycle.
SI unit: second (s).
Wave Speed
Wave speed is the speed at which the disturbance travels through a medium or space.
SI unit: metre per second (m/s).
Transverse and Longitudinal Waves
| Feature | Transverse wave | Longitudinal wave |
|---|---|---|
| Particle motion | Perpendicular to the direction of wave travel | Parallel to the direction of wave travel |
| Main features | Crests and troughs | Compressions and rarefactions |
| Example | Wave on a stretched rope | Sound in air |
A sound wave travelling through air is usually described as a longitudinal pressure wave. Air particles vibrate back and forth, producing alternating regions of high pressure called compressions and low pressure called rarefactions.
Core Wave Formulas
1. Wave Speed, Frequency, and Wavelength
v = fλ
- v = wave speed in metres per second (m/s)
- f = frequency in hertz (Hz)
- λ = wavelength in metres (m)
This formula is used when two of the three quantities are known and the third must be calculated. It also shows that, when wave speed is constant, frequency and wavelength are inversely related: a higher frequency means a shorter wavelength.
Example: Finding the Wavelength of Sound
Given:
- Speed of sound, v = 343 m/s
- Frequency, f = 500 Hz
Formula:
λ = v ÷ f
Substitution:
λ = 343 m/s ÷ 500 Hz
λ = 0.686 m
Final answer: The wavelength is 0.686 m.
2. Frequency and Period
f = 1/T
The rearranged form is:
T = 1/f
- f = frequency in hertz (Hz)
- T = period in seconds (s)
Use these relationships when you need to convert between the number of cycles per second and the time for one cycle.
Example: Finding the Period
Given: A wave has a frequency of 50 Hz.
Formula: T = 1/f
Substitution: T = 1 ÷ 50 Hz
Calculation: T = 0.020 s
Final answer: The period is 0.020 s.
What Is Sound?
Sound is a mechanical wave produced by a vibrating object. The vibration creates pressure changes in a medium, such as air, water, or a solid. These pressure changes travel outward and may be detected by the ear or by a sensor.
Sound cannot travel through a vacuum because a vacuum has no particles to vibrate and pass the disturbance along. This is why an explosion in space cannot be heard directly by a person who is not connected to it by a medium or communication system.
Important Point
Sound transfers energy through a medium, but the medium’s particles generally vibrate around their positions rather than travelling with the sound from the source to the listener.
How Sound Is Described
Pitch and Frequency
Pitch describes how high or low a sound seems. It is mainly related to frequency. A high-frequency sound has a high pitch, while a low-frequency sound has a low pitch.
Loudness and Amplitude
Loudness describes how strong a sound seems to a listener. It is related to the wave’s amplitude and intensity. A greater amplitude generally produces a louder sound.
Timbre
Timbre is the quality or character of a sound. It allows us to distinguish two instruments playing the same note at the same loudness. Timbre depends on the mixture of frequencies in the sound.
Speed of Sound
The speed of sound depends on the medium and its physical conditions. Sound generally travels faster through solids than through liquids and faster through liquids than through gases. In a gas, temperature can also affect the speed of sound.
The frequency of a sound is determined by its source. When sound enters a different medium, its speed and wavelength may change, but the frequency normally remains the same because the source is still vibrating at the same rate.
Common Confusion
A louder sound does not normally travel faster than a softer sound in the same medium. Loudness is related mainly to amplitude, while speed is determined mainly by the medium and its conditions.
Sound Intensity and the Decibel Scale
Sound intensity is the sound power transmitted through each unit area. It describes how much energy passes through a given area every second.
3. Sound Intensity
I = P/A
- I = intensity in watts per square metre (W/m²)
- P = power carried by the wave in watts (W)
- A = area over which the power is spread in square metres (m²)
Use this formula to calculate the intensity when the power and area are known.
Example: Calculating Sound Intensity
Given:
- Sound power, P = 0.20 W
- Area, A = 4.0 m²
Formula: I = P/A
Substitution: I = 0.20 W ÷ 4.0 m²
Calculation: I = 0.050 W/m²
Final answer: The sound intensity is 0.050 W/m².
4. Sound Intensity Level
β = 10 log10(I/I0)
- β = sound intensity level in decibels (dB)
- I = sound intensity in watts per square metre (W/m²)
- I0 = reference intensity, usually 1 × 10−12 W/m²
This formula is used to express sound intensity on the logarithmic decibel scale. A change of 10 dB corresponds to a factor of 10 change in intensity.
Example: Finding the Sound Level
Given:
- I = 1 × 10−6 W/m²
- I0 = 1 × 10−12 W/m²
Formula: β = 10 log10(I/I0)
Substitution:
β = 10 log10[(1 × 10−6)/(1 × 10−12)]
β = 10 log10(106)
β = 10 × 6
Final answer: β = 60 dB.
Decibels Are Not the Same as Loudness
The decibel is a logarithmic physical scale. Human perception of loudness also depends on frequency, distance, the environment, and the individual listener. Therefore, two sounds with the same measured level may not seem equally loud in every situation.
Human Hearing and Other Sound Frequencies
The commonly stated audible range for a young human listener is approximately 20 Hz to 20,000 Hz. The actual range varies with age and individual hearing ability.
| Type of sound | Frequency range | Example or use |
|---|---|---|
| Infrasound | Below about 20 Hz | Some natural events and large vibrations |
| Audible sound | Approximately 20 Hz to 20 kHz for young human hearing | Speech, music, and everyday sounds |
| Ultrasound | Above about 20 kHz | Medical imaging, industrial testing, and some animal communication |
Wave Behaviours
Reflection
Reflection occurs when a wave bounces back after reaching a boundary. Sound reflection can produce an echo. Hard, smooth surfaces usually reflect sound effectively.
Refraction
Refraction is the change in direction or speed of a wave when it enters a region or medium where its speed changes. Changes in air temperature can affect the path of sound.
Diffraction
Diffraction is the spreading or bending of waves around obstacles and through openings. Sound can sometimes be heard around a doorway because sound waves spread into regions that are not directly in line with the source.
Interference
Interference occurs when waves overlap. Constructive interference can increase the resulting amplitude, while destructive interference can reduce it.
Resonance and Standing Waves
Resonance occurs when an object is driven at or near one of its natural frequencies. The object can then vibrate with a much greater amplitude.
Musical instruments use resonance to strengthen sound. For example, the air inside a pipe or the body of a string instrument can vibrate strongly at particular frequencies.
A standing wave can form when incident and reflected waves interfere in a fixed pattern. A standing wave has stationary points called nodes and points of maximum vibration called antinodes.
Practical Examples of Resonance
- A guitar body helps amplify the vibration of its strings.
- Air columns in pipes support particular musical notes.
- Ultrasound systems use controlled vibrations at high frequencies.
How Musical Instruments Produce Different Sounds
- A vibrating part produces the initial sound, such as a string, reed, membrane, or column of air.
- The vibration causes pressure changes in the surrounding medium.
- The instrument’s shape and material affect resonance and the mixture of frequencies.
- The listener’s ear detects the pressure variations and the brain interprets them as sound.
Changing the vibrating length or tension of a string changes its frequency and therefore changes the pitch. Changing the strength of the vibration mainly changes the amplitude and therefore affects the sound’s intensity.
Applications of Waves and Sound
- Communication: microphones, telephones, radios, and loudspeakers convert sound or electrical signals.
- Medical imaging: ultrasound uses high-frequency sound waves to produce images inside the body.
- Navigation: sonar uses reflected sound waves to detect underwater objects and measure distances.
- Engineering testing: sound and ultrasound can help detect cracks or changes inside materials.
- Architecture: the reflection and absorption of sound are considered when designing classrooms, theatres, and recording studios.
- Earth science: seismic waves help scientists investigate the structure of Earth.
Common Mistakes and Misconceptions
- “A wave transports matter from source to destination.” Usually, the wave transfers energy while particles of the medium oscillate around their positions.
- “Sound can travel through empty space.” Sound needs a material medium, so it cannot travel through a vacuum.
- “High pitch means loud sound.” Pitch is mainly related to frequency. Loudness is mainly related to amplitude and intensity.
- “A larger wavelength always means a faster wave.” Wave speed depends on the medium. The relationship is v = fλ.
- “Decibels can be added like ordinary numbers.” Decibels use a logarithmic scale, so sound levels cannot usually be combined by simple arithmetic addition.
- “Frequency changes whenever a sound enters a new medium.” The frequency normally remains determined by the source, while speed and wavelength may change.
Important Points to Remember
- Waves transfer energy from one place to another.
- Sound is a mechanical, usually longitudinal, wave.
- Sound requires a medium and cannot travel through a vacuum.
- Amplitude describes maximum displacement and is related to energy and loudness.
- Frequency is measured in hertz and is related to pitch.
- Wavelength is measured in metres.
- The main wave relationship is v = fλ.
- Frequency and period are related by f = 1/T.
- Sound intensity is power per unit area: I = P/A.
- Sound intensity level is measured on a logarithmic decibel scale.
- Reflection, refraction, diffraction, interference, and resonance are important wave behaviours.
Quick Recap
Waves are travelling disturbances that transfer energy. Sound is produced by vibrations and travels through a material medium as changing pressure. The important quantities are amplitude, frequency, period, wavelength, and wave speed. They are connected by v = fλ and f = 1/T. Sound’s pitch depends mainly on frequency, while loudness is related mainly to amplitude and intensity. Sound can reflect, refract, diffract, interfere, and resonate. These principles explain everyday sounds, musical instruments, hearing, communication, medical ultrasound, sonar, and many engineering applications.