Sound Waves: Frequency and Pitch

• Sound waves are longitudinal waves, meaning the particles of the medium vibrate parallel to the direction of energy transport
• Characterized by compressions (regions of high pressure) and rarefactions (regions of low pressure)

Frequency

• Refers to the number of complete cycles of a wave occurring per unit of time, typically measured in Hertz (Hz)
• One Hertz (Hz) equals one cycle per second
• Higher frequency sound waves correspond to more cycles per second
• Frequency determines the pitch of a sound

Pitch

• Subjective perception of the frequency of a sound
• High-frequency sound waves are perceived as high-pitched sounds
• Low-frequency sound waves are perceived as low-pitched sounds
• Primarily determined by frequency, but intensity and timbre can also influence perception

Audible Range

• The human ear can typically hear sounds within a frequency range of approximately 20 Hz to 20,000 Hz (20 kHz)
• Varies depending on age, exposure to loud noises, and other individual factors
• Frequencies below 20 Hz are called infrasound, while frequencies above 20 kHz are called ultrasound
• Some animals can hear frequencies outside the human audible range; for example, dogs can hear ultrasound

Relationship between Frequency and Wavelength

• The speed of a sound wave (v) is related to its frequency (f) and wavelength (λ) by the equation v = fλ
• Wavelength is the distance between two consecutive compressions or rarefactions in a sound wave
• At a constant speed, frequency and wavelength are inversely proportional: higher frequency means shorter wavelength, and lower frequency means longer wavelength

Factors Affecting Frequency

• Depends on the physical properties of the object such as its size, mass, tension, and stiffness
• A shorter and tighter guitar string vibrates at a higher frequency than a longer and looser string
• Affected by the medium through which they travel, particularly by the medium's density and elasticity

Applications of Frequency and Pitch

• Musical instruments are designed to produce specific frequencies to create different musical notes and tones
• Medical ultrasound uses high-frequency sound waves to create images of internal body structures
• Communication systems, such as telephones and radios, use different frequencies to transmit and receive information
• Pitch detection and manipulation are used in audio processing and music production

Complex Sounds and Harmonics

• Most real-world sounds are complex, consisting of multiple frequencies rather than a single pure tone
• The fundamental frequency is the lowest frequency component of a complex sound and determines the perceived pitch
• Harmonics (or overtones) are frequencies that are multiples of the fundamental frequency and contribute to the timbre (or tone color) of the sound
• The presence and relative amplitudes of different harmonics give each sound its unique characteristic

Doppler Effect

• The change in frequency (and thus pitch) of a sound wave due to the relative motion between the source of the sound and the observer
• When a sound source moves toward an observer, the frequency appears higher (higher pitch)
• When a sound source moves away from an observer, the frequency appears lower (lower pitch)
• Used in various applications, such as radar and medical imaging, to measure velocities and distances

Measurement of Frequency

• Can be measured using electronic instruments such as oscilloscopes, frequency counters, and spectrum analyzers
• These instruments analyze the waveform of the sound and determine the number of cycles per second
• Computer software can also be used to perform frequency analysis of audio recordings

Subjective Perception

• While frequency is an objective physical property of sound waves, pitch is a subjective perception that varies from person to person
• Factors such as age, hearing ability, and cognitive factors can influence how we perceive pitch
• Some individuals have perfect pitch (absolute pitch), the ability to identify or produce a specific musical note without any reference

Frequency Range of Instruments and Voices

• Different musical instruments and human voices have different frequency ranges
• A piano can produce frequencies ranging from about 27 Hz to 4186 Hz
• The typical male voice ranges from about 85 Hz to 180 Hz, while the typical female voice ranges from about 165 Hz to 255 Hz

Sound Quality

• Frequency and pitch are important aspects of sound quality
• Altering the frequencies present in a sound can significantly change its perceived character
• Adjusting frequency levels in audio mixing is a key component to creating balanced and pleasing sounds

Frequency Analysis Tools

• Frequency analysis can be performed through various tools
• Spectrum analyzers are used to visualize the frequency components of a signal
• Spectrograms show how the frequencies in a sound vary over time
• Fourier transforms are mathematical techniques used to decompose a signal into its constituent frequencies