Chapter 15

Properties of Sound

Properties of Sound Waves Sound is a compression wave in any material medium oscillating within the frequency range of 20 Hz to 20 kHz. Sound waves are longitudinal and can propagate as a sphere in an elastic medium such as air.

Properties of Sound Waves Amplitude determines loudness Frequency determines pitch **Most sounds you hear are multi-frequency combinations superimposed to create complex wave patters**

Categories of Sound Waves Audible waves Lay within the normal range of hearing of the human ear Normally between 20 Hz to 20,000 Hz Infrasonic waves Frequencies are below the audible range Earthquakes are an example Ultrasonic waves Frequencies are above the audible range Dog whistles are an example

Measuring Sound

Intensity The rate of transfer of energy is the acoustic power. A person speaking at a normal conversational level emits power at about J/s and shouts at about 1 mJ/s. The Intensity (I) of a wave is defined as the average power divided by the perpendicular area across which it is transported. Intensity has units of W/m 2. As a spherical wave expands outward, its area (4  R 2 ) increases, the intensity diminishes inversely with the square of the radius – Inverse Square Law

Loudness Loudness depends on the frequency, duration, and intensity of the sound. We judge the relative loudness of a sound not by the difference in intensity between it and some reference but by their ratio. Multiplying any intensity by 10 will generally be perceived as approximately doubling it in loudness; W/m 2 sounds twice as loud as W/m 2 – the ear responds logarithmically.

Sound-Level The sound-level (or intensity-level) of an acoustic wave is defined as the number of factors of 10 that its intensity is above the threshold of hearing: I 0 = 1.0 X W/m 2. The unit of sound intensity-level is called the bel. A decibel (abbreviated dB) is 1/10 of a bel and is unitless. By definition, the logarithm to the base 10 of any number X equals the power to which 10 must be raised to equal X In other words, if X = 10 Y, then the log 10 X = Y = 10 3 and so log = 3.

Sound-Level The intensity-level  in dB of any sound is For example, a sound wave with an intensity of W/m 2 has an intensity-level of Increasing the intensity by a factor of 10 changes the sound-level by 1 bel or 10 dB.

Frequency Response Curves Bottom curve is the threshold of hearing Threshold of hearing is strongly dependent on frequency Easiest frequency to hear is about 3300 Hz When the sound is loud (top curve, threshold of pain) all frequencies can be heard equally well

Example 1 A faint sound with an intensity of W/m 2 is measured by a sound-level meter—what will be the reading in dB?

Example 2 Two public address systems are being compared, and one is perceived to be 32 times louder than the other. What will be the difference in sound levels between the two when measured by a dB-meter? Given: a factor of 32 in loudness Find: ∆ 

Example 2 Solution: Sound level problem. Given a change in loudness – note that a doubling in loudness is approximately the same as multiplying the intensity by 10 – by equation this would be about a change of 10 dB. Since 32 = 2 5 – the loudness is doubled five times. So the difference in sound levels (∆  ) is 5 times the 10 dB. ∆  = 5(10 dB) = 50 dB

Sound Waves

Sound behaves like any other wave, having: Frequency – 20Hz – 20,000Hz (audible) Wavelength – relatively long, in the centimeter to meter range measured between successive areas of high or low pressure Velocity – which remains constant in any given medium (343 m/s in air: 660 mi/hr), therefore wavelength and frequency trade off

Velocity of Sound v = 330m/s; 660 miles/hour in “typical conditions” v increases with increasing temperature and pressure v increases in s lighter medium (hydrogen as opposed to air) v increases sharply as sound passes into liquids and again in solids (about double each time).

Example 3 By international agreement, most orchestras tune to a frequency of 440 Hz, which is called A440 (the A note above middle C). Given that the speed of sound in air at room temperature is m/s, what is the wavelength of A440? Given: f = 440 Hz and v = m/s Find:

Example 3 Solution: f, v, and are related.

Doppler Effect A Doppler effect is experienced whenever there is relative motion between a source of waves and an observer. When the source and the observer are moving toward each other, the observer hears a higher frequency When the source and the observer are moving away from each other, the observer hears a lower frequency

Doppler Effect, cont. Although the Doppler Effect is commonly experienced with sound waves, it is a phenomena common to all waves Assumptions: The air is stationary All speed measurements are made relative to the stationary medium

Doppler Effect, Case 1 An observer is moving toward a stationary source Due to his movement, the observer detects an additional number of wave fronts The frequency heard is increased (Observer Toward Source)

Doppler Effect, Case 1 An observer is moving away from a stationary source The observer detects fewer wave fronts per second The frequency appears lower (Observer Away from Source)

Doppler Effect, Case 1 – Equation When moving toward the stationary source v s =0, the observed frequency is When moving away from the stationary source, the observed frequency is When source is stationary

Case 1 – Equation, General When moving toward a moving source v s, the observed frequency is When moving away from a moving source, the observer’s frequency is When source is not stationary

Overall CONSIDER A LINE FROM THE OBSERVER TO THE SOURCE THIS IS THE POSITIVE DIRECTION V O AND V S ARE ASSIGNED + OR - ACCORDINGLY

Example 4 An automobile traveling at 20.0 m/s (45 mph) blows a horn at a constant 600 Hz. Determine the frequency that will be perceived by a stationary observer both as the car (a) approaches and (b) recedes. Take the speed of sound to be 340 m/s. Given: v s = 20.0 m/s, v o = 0, v = 340 m/s, and f S = 600 Hz Find: f o

Example 4 Solution: This is a Doppler effect problem, use equations The source is approaching, use – v s in Eq. (11.23) 638 Hz The source is receding, use + v s in Eq. (11.23) 567 Hz

Doppler Effect, General Case Both the source and the observer could be moving Use positive values of v o and v s if the motion is toward Frequency appears higher Use negative values of v o and v s if the motion is away Frequency appears lower

Example 5 A Police care with its siren blaring at 1000Hz is chasing a truck. The police car is traveling at 20m/s, and the truck is traveling at 15m/s. What frequency does the truck driver actually hear as the police car catches up to him? Assume the speed of sound in air on this occasion is 330m/s.

Standing Waves in Air Columns If one end of the air column is closed, a node must exist at this end since the movement of the air is restricted For an “E” note of 660Hz and v = 330m/s the wavelength is then 0.52m and the pipe needs to be 0.13m to create the fundamental

Tube Closed at One End

Standing Waves in Air Columns If BOTH ends are open, then antinodes will form at both ends and the pipe will need to be one half the wavelength. For the same “E” note then (660Hz, 330m/s, λ = 0.52m) the pipe needs to be 0.26m long to create the fundamental.

Tube Open at Both Ends

Reverberation The multiple-echo effect of reflected sound waves bouncing off the boundaries in an enclosed space. When designed correctly, the space enhances the sound. When designed poorly, the space muddies the sound. Dead spots may be created where destructive interference takes place.

Reverberation

Fourier’s Theorem Any complex wave pattern can be represented by the addition of multiple, single-frequency waves called component frequencies.

Frequency Spectrum

Hearing Sound The outer ear consists of the ear canal that terminates at the eardrum Just behind the eardrum is the middle ear The bones in the middle ear transmit sounds to the inner ear The Ear

Pitch Pitch is related mainly, although not completely, to the frequency of the sound Pitch is not a physical property of the sound Frequency is the stimulus and pitch is the response It is a psychological reaction that allows humans to place the sound on a scale

Timbre In music, the characteristic sound of any instrument is referred to as the quality of sound, or the timbre, of the sound The quality depends on the mixture of harmonics in the sound A flute, a trumpet, a saxophone, or a tuning fork, can produce the same note (same pitch) at the same loudness, but have a different timbre, which depends on the waveform. **Different instruments have different timbre because they produce different Fourier spectra**

Scales A series of frequencies occurring at set intervals

Harmony Harmony is a combination of frequencies which produce a new musical tone. Consonance – a GOOD combination of frequencies Dissonance -- a BAD combination of frequencies Beats – occur as a pulsating amplitude created by certain frequency combinations

Beats Beats are alternations in loudness, due to interference Waves have slightly different frequencies and the time between constructive and destructive interference alternates The beat frequency equals the difference in frequency between the two sources: