Chapter 14: Sound and Hearing

Chapter 14: Sound and Hearing

• Sound is a disturbance of matter transmitted outward from its source.
• Sound waves are longitudinal waves consisting of alternating compressions and rarefactions.
• Frequency of a sound, f, is the number of complete waves passing a point per unit time (measured in Hz).
• Wavelength, λ, is the distance between two consecutive compressions or rarefactions.
• The speed of sound, v, is the rate at which the wave travels. The relationship is: v = λf .
• The speed of sound depends on the medium and its temperature.
• Sound travels faster in solids than in liquids and faster in them than in gases, and faster at higher temperatures in all states of matter.
• Humans can hear frequencies ranging from 20 Hz to 20,000 Hz.

What is Sound?

• A vibrating tuning fork creates a series of compressions and rarefactions in the air.
• The crests of the wave correspond to compressions, the troughs to rarefactions.
• A vibrating source transfers energy to surrounding molecules.
• This energy is used to compress and expand the surrounding medium.
• High pressure regions are called compressions, low pressure regions are called rarefactions.

Loudness & Intensity

• Loudness is related to the energy of the source and the distance.
• Loudness is proportional to intensity, which is power per unit area (W/m²).
• Intensity of a point source varies inversely with the square of the distance from the source.
• The measurement of loudness, or intensity level is in decibels (dB).

Speed of Sound

• The speed of sound is usually given as dependent on the temperature and type of medium.
• The speed of sound at sea level is approximately 331 m/s at 0° Celsius (273 Kelvin)
• The formula is: v = λf.
• Speed of sound is approximately independent of frequency.

Threshold of Hearing & Pain

• Threshold of hearing: The faintest sound a human can hear (0 decibels).
  The intensity is 1x10^-12 W/m².
• Threshold of pain: The loudest sound a human can tolerate without causing pain (approximately 120–130 dB). Intensity is approximately 1 W/m².

Intensity vs Loudness

• Human perception of loudness is logarithmic, not linear.
• One important logarithmic scale is decibels (dB).
• A 10dB change corresponds to a change in intensity by a factor of 10 (e.g. from 20dB to 30dB).

Doppler Effect

• A change in the observed frequency of a sound due to the motion of the source and/or observer.
• The frequency observed by a stationary observer increases as the source approaches and decreases as it moves away.

Standing Waves

• When waves of equal frequency and amplitude travel in opposite directions, standing waves are created.
• Sound waves from a source may interfere with reflected waves, producing standing waves.
• The amplitude of the vertical oscillation of any element of the string depends on the horizontal position of the element.
• The wavelength of the fundamental standing wave in a string fixed at both ends is twice the length of the string.
• A standing wave in a tube open at one end has one antinode at the open end and a node at the other end.
• A standing wave in a tube open at both ends has antinodes at both ends.

Beats

• Beats are an interference pattern that results from the superposition of two sound waves with slightly different frequencies.
• The beat frequency is the difference between the frequencies of the two interfering waves.