Physics 36 / Music 36 Duke University Spring 2008 Handout 7
Extracted from the liner notes [by A. J. M. Houtsma, T. D. Rossing, and W. M. Wagenaars, IPO, Eindhoven, The Netherlands, 1987] for the American Institute of Physics demonstration CD adapted for use in class.
The various demonstrations are discussed in the order in which they will be presented in class. Where phenomena are discussed in more detail later in these notes, a hypertext link is provided to the later material. The demonstrations are numbered to help you associate the responses you record in class with these notes. Any specific data to be recorded in class are noted in italics at the end of the respective demonstration's description. The class demonstrations will be much more valuable to you if you study these notes beforehand.
How long must a tone be heard in order to have an identifiable pitch? Early experiments indicated that a sense of pitch develops after only two cycles. Very brief tones are described as "clicks," but as the tones lengthen, the clicks take on a sense of pitch which increases upon further lengthening.
It has been suggested that the dependence of pitch salience on duration
follows a sort of "acoustic uncertainty principle",
, where
is the uncertainty in frequency and 
is the duration of a tone burst. K, which can be as short as 0.1, appears
to depend upon intensity and amplitude envelope. The actual pitch appears
to have little or no dependence on duration.
In this demonstration, we present tones of 300, 1000, and 3000 Hz in bursts of 1, 2, 4, 8, 16, 32, 64, and 128 periods (complete cycles). Record how many periods are necessary to establish a sense of pitch in each case. You can also calculate the corresponding burst durations, to see whether your perception depends more on absolute duration than number of periods.
How does the loudness of an impulsive sound compare with the loudness of a steady sound at the same sound level? Numerous experiments have pretty well established that the "ear" averages sound energy over about 0.2 s (200 ms), so loudness grows with duration up to this value, loudness level increasing by 10 dB when the duration is increased by a factor of 10. The loudness level of broadband noise seems to depend somewhat more strongly on stimulus duration than the loudness level of pure tones.
In this demonstration, bursts of broadband noise having durations of 1000, 300, 100, 30, 10, 3, and 1 ms are presented at 8 decreasing levels (0, -16, -20, -24, -28, -32, -36, and -40 dB) in the presence of a broadband masking noise. Count the number of steps you are able to hear in each case.
The ability to distinguish between two nearly equal stimuli is often characterized by a difference limen (DL) or a just noticeable difference (jnd). Two stimuli cannot be consistently distinguished from one another if they differ by less than a jnd. The jnd for pitch has been found to depend on the frequency, the sound level, the duration of the tone, and the suddenness of the frequency change. Typically, it is found to be about 1/30 of the critical bandwidth at the same frequency.
In this demonstration, 10 groups of 4 tone pairs are presented. For each pair, the second tone may be higher or lower than the first tone. Pairs are presented in random order within each group, and the frequency difference decreases by 1 Hz in each successive group, from 10 Hz to 1 Hz. One of the tones of each pair has a frequency of 1000 Hz. Record whether the second tone of each pair seems higher ("H") or lower ("L") than the first. Start a new line in your notes for each set of four pairs.
Establishing a scale of subjective loudness requires careful psychoacoustical experimentation involving large numbers of subjects. A scale of sones has been used widely to describe subjective loudness. On this scale, the loudness in sones S is proportional to sound pressure p raised to the 0.6 power: S = Cp0.6, where C depends on the frequency. In other words, the loudness doubles for about a 10 dB increase in sound pressure level. Some investigators have found that the exponent varies with tone frequency, increasing at low frequency and low level to approach a value of 1.0. [An exponent of 1.0 would mean that loudness doubled for a 6 dB increase in sound pressure level.]
In this demonstration, a reference sound of broadband noise alternates with similar sounds having levels of 0, ±5, ±10, ±15, or ±20 dB with respect to the reference tone. The tones are 1 s long, separated by 250 ms of quiet, and the trials are separated by 2.25 s of quiet. To help establish a scale, the reference tone is first presented along with the strongest and weakest sound that will be heard. Think of the reference tone as having a loudness of "100". Then a test tone you hear as twice as loud as the reference tone would be designated as "200", and a test tone half as loud as the reference would be "50", etc. For each of the 20 pairs, write down a number reflecting the loudness of the second (test) tone relative to the reference. Hand in your data; they will be plotted with those of the rest of the class so we can see whether we share a consensus as to subjective loudness judgments.
Early experimenters (c 1935) reported substantial pitch dependence on intensity (12% pitch shifts for sinusoidal tones increasing from 40 to 90dB in intensity). More recent work indicates that, while some individuals perceive such large pitch changes, the effect varies considerably from person to person.
In this demonstration, we use 500 ms tone bursts having frequencies of 200, 500, 1000, 3000, and 4000 Hz. Six pairs of tones are presented at each frequency, with the second tone of each pair having a level that is 30 dB higher than the first (which is itself 5 dB above the preliminary 200 Hz calibration tone). For most people and most pairs, a slight pitch change will be audible. Write down whether the second tone of each pair is higher in pitch (H), the same (S), or lower in pitch (L).
Perception (e.g. visual, auditory) is an interpretive process. If our view of one object is obscured by another, for example, our perception may be that of two intact objects, even though this information is not present in the visual image. In general, our interpretive processes provide us with an accurate picture of the world; occasionally, as in the case of visual or auditory illusions, they can be fooled.
Such interpretive processes can be demonstrated by alternating a sinusoidal signal with bursts of noise. Whether the signal is perceived as pulsating or continuous depends upon the relative intensities of the signal and noise.
In this demonstration, 125 ms bursts of a 2000 Hz tone alternate with 125 ms bursts of noise (a 1875-2125 Hz band of noise). The noise level remains constant, while the tone level decreases in 15 steps of -1 dB after each 4 tones. The pulsation threshold is given by the level at which the 2000 Hz tone begins to sound continuous. Count in how many of the cases the pulse bursts seem to interrupt the tone.
A pure tone masks tones of higher frequency more effectively than tones of lower frequency. This demonstration uses tones of 1200 and 2000 Hz, presented as 200 ms tone bursts separated by 100 ms. The unchanging masker is part of every pulse, while the test tone, added to every other pulse, decreases in 10 steps of 5 dB each, except the first step which is 15 dB. First the masker is 1200 Hz and the test tone is 2000 Hz, then the masker is 2000 Hz and the test tone 1200 Hz. Count how many steps of the test tone can be heard in each case.
Masking can occur even when the tone and the masker are not simultaneous. Forward masking refers to the masking of a tone by a sound that ends a short time (up to about 20 or 30 ms) before the tone begins. This effect suggests that recently stimulated sensors are not as sensitive as fully-rested ones. Backward masking refers to the masking of a tone by a sound that begins after the tone has ended (up to 10 ms later, but the amount of masking decreases as the time interval increases). This effect apparently occurs at higher centers of processing in the nervous system where the neural correlates of the later-occurring stimulus of greater intensity overtake and interfere with those of the weaker, earlier stimulus.
In this demonstration, the signal (10 ms bursts of a 2000 Hz sinusoid) first is presented in 10 decreasing steps of -4 dB without a masker. Next, the 2000 Hz signal is followed after a time gap t by a 250 ms burst of noise (1900-2100 Hz), alternating with the noise burst alone. The time gap t is successively 100 ms, 20 ms, and 0. Finally, the masker is presented before the tone, again with t = 100 ms, 20 ms, and 0. Count the number of steps for which you can hear the brief signal preceding or following the noise.
The pitch of a tone is influenced by the presence of masking noise or another tone near to it in frequency. If the interfering tone has a lower frequency, an upward shift in the test tone is always observed. If the interfering tone has a higher frequency, a downward shift is observed, at least at low frequency (< 300 Hz). Similarly, a band of interfering noise produces an upward shift in a test tone if the frequency of the noise is lower.
In this demonstration, a 1000 Hz tone, 500 ms in duration and partially masked by noise (low-pass filtered to include only frequencies below 900 Hz), alternates with an identical tone, presented without masking noise. The tone partially masked by noise of lower frequency appears slightly higher in pitch: do you agree? When the noise is turned off, it is clear that the two tones were identical.
This demonstration uses a cyclic set of complex tones, each composed of 10 partials separated by octave intervals. The tones are filtered to produce a constant distribution of sound level as a function of frequency. The frequencies of the partials are shifted upward in steps corresponding to a musical semitone (about 6%). The result is the illusion of an "ever-ascending" scale.
It is clear in listening to melodies that sequences of tones can form coherent patterns. This is called temporal coherence. When tones do not form patterns, but seem isolated, that is called fission.
In this demonstration we present two tones, A and B, in the sequence ABA ABA etc. Tone A always has a frequency of 2000 Hz, while tone B varies from 1000 to 4000 Hz and back again. Near the crossover points, the tones appear to form a coherent pattern, characterized by a "galloping" rhythm, but at large intervals the tones seem isolated, illustrating fission.
In the first part of this demonstration, we hear broadband noise reduced in steps of 6, 3, and 1 dB in order to obtain a feeling for the decibel scale . In the latter part, a voice is heard at distances of 25, 50, 100, and 200 cm from an omni-directional microphone in an anechoic chamber. Under these conditions, the sound pressure level decreases about 6 dB each time the distance is doubled. [In a normal room this will not be the case, because of reflections from walls, ceiling, floor, and objects in the room.]
Although sounds with greater sound pressure level usually sound louder, this is not always the case. The sensitivity of the ear varies with the frequency and the quality of the sound. In their famous experiments of 1933, Fletcher and Munson determined curves of equal loudness for pure tones, demonstrating the relative insensitivity of the ear to sounds of low frequency at moderate to low intensity levels. Hearing sensitivity reaches a maximum around 4000 Hz, which is near the first resonance frequency of the outer ear canal, and again peaks around 12 kHz, the frequency of the second resonance.
In this demonstration, we compare the thresholds of audibility (in a room) for tones having frequencies of 125, 250, 500, 1000, 2000, 4000, and 8000 Hz. The tones are 100 ms in length and decrease in 10 steps of -5 dB each. Naturally, the threshold of audibility in a room depends very much on the character of the background noise. Nevertheless, in most rooms the threshold should increase measurably at low frequency. Also, remember that pure tones cause standing waves in a room that can produce sound level differences of 10 dB or more--so sit still during the demonstration! Count the number of steps you hear at each frequency.
In this demonstration, a single 2000 Hz tone is masked by spectrally flat (white) noise of different bandwidths--first broadband noise and then bandwidths of 1000, 250, and 10 Hz. In order to determine the level of the tone that can just be heard in the presence of the noise, in each case, we present the 2000 Hz tone in 10 decreasing steps of 5 dB each.
Since the critical bandwidth at 2000 Hz is about 280 Hz, you would expect to hear more steps in the 2000 Hz staircase when the noise bandwidth is reduced below this value. [Note that since the spectrum level of the noise is kept constant, its intensity--and its subjective loudness--will decrease markedly as the bandwidth is decreased.] Count how many steps you can hear in each case.
This demonstration provides another method for estimating critical bandwidth. The bandwidth of a noise burst is increased while its amplitude is decreased to keep the power constant. When the bandwidth is greater than a critical band, the subjective loudness increases above that of a reference noise burst, because the stimulus now extends over more than one critical band.
A reference noise band, centered at 1000 Hz and with a 15% bandwidth (930-1075 Hz) is followed by a test band with the same center frequency and bandwidth. In subsequent pairs, the bandwidth of the test band is increased in 7 steps of 15% each, while the amplitude is decreased to keep the power constant. When the bandwidth exceeds the critical bandwidth at 1000 Hz, the loudness begins to increase. Compare the loudness of the reference and test bands in each pair.
