Scholars Commons @ Laurier Scholars Commons @ Laurier Urgency is a Non-monotonic Function of Pulse Rate Urgency is a Non-monotonic Function of Pulse Rate

: Magnitude estimation was used to assess the experience of urgency in pulse-train stimuli (pulsed white noise) ranging from 3.13 to 200 Hz. At low pulse rates, pulses were easily resolved. At high pulse rates, pulses fused together leading to a tonal sensation with a clear pitch level. Urgency ratings followed a nonmonotonic (polynomial) function with local maxima at 17.68 and 200 Hz. The same stimuli were also used in response time and pitch scaling experiments. Response times were negatively corre-lated with urgency ratings. Pitch scaling results indicated that urgency of pulse trains is mediated by the perceptual constructs of speed and pitch.


s, increasing
the speed (i.e., decreasing the inter-onset time; Edworthy et al., 1991;Guillaume et al., 2003;Hellier et al., 1993).Research has conventionally framed these two influences on the experience of urgency as independent and their effects have been compared directly using psychophysical methods.For example, applying Stevens' power law, Hellier and Edworthy (1999) found that larger changes to pitch than to speed were necessary in order to yield eq ivalent changes in experienced urgency (slopes of 0.37 and 1.35, respectively).

However, from a strictly temporal perspective, frequency and inter-onset time of auditory warnings may be interpreted as reciprocals of one another falling along different ends of the same rate-based continuum; that is, faster pulse rates (in terms of cycles per second or event onsets) tend to convey higher levels of urgency.Ecological psychoacoustics may provide a unifying framework for understanding rate-based predictors of urgency (Neuhoff, 2004).Specifically, it may be argued that it is not necessary to have mediation by mental representations of the physical world (such as conceptions about pitch or speed) in order to experience something as urgent or to act on it appropriately (Gibson, 1979).A related possibility is that the experience of urgency is based upon familiarity with probabilistic cues inherent in emotional speech.L steners appear to perceive elevations in speech rate, pitch, or both not in terms of acoustics but in terms of a speaker's level of arousal (Scherer, 1986).In sum, it is possible that perceptual mediation is not necessary to experience urgency and that a single monotonic function can be used to characterize both rate-based predictors.

In this study, we addressed the role of perceptual mediation and whether psychometric functions concerning different rate-based predictors of urgency are truly independent.This question was assessed by developing a continuum of pulse-train stimuli that varied only in rate (Miller and Taylor, 1948).At the low end of the continuum, pulses were easily resolved, with changes in rate corresponding to speed (or tempo).At the high end of the continuum, pulses fused together perceptually leading to a tonal sensation with a clear pitch level.To our knowledge, this is the first study of urgency incorporating phenomenological changes in speed and pitch along a single rate-based continuum.


Urgency scaling experiment

A magnitude estimation task was conducted to assess the experienced urgency of pulse trains that varied in rate between 3.13 and 20 Hz.


Participants

Thirty participants (20 women and 10 men) with normal hearing were asked to provide magnitude estimations.The mean age of participants was 21 years (SD= 1.9 years).The procedures were approved by the Wilfrid Laurier University Research Ethics Board and all participants gave informed consent.


Stimuli and apparatus

Pulses (bursts of white noise) were interleaved with silent intervals (of equal duration) at varying rates of repetition.The rate of the resulting pulse train was thus determined by the interonset-interval of the noise burst.Rates were equally spaced on a log scale ranging from 3.13 to 200 Hz.Sounds were presented in a double-walled sound-attenuated

amber over headphones (Sony
Stereo Headphones MDR-XD200) at a presentation level of 70 dB SPL.


Procedure

Each sound was presented for a duration of 2.5 s with the

rder of sound
being independently randomized for each participant.Participants judged the experienced urgency of each sound using a free-modulus magnitude estimation task (Stevens, 1975) in which participants are asked to assign a numerical value to each sound.The absence of a fixed scale (e.g., 1 to 7) imp

ves sensitivity of mea
urement by encouraging participants to actively compare each response to all other responses.Participants' responses initiated the following trial and each session lasted approximately 15 min.


Results and discussion

Responses of each participant were first standardized (converted to z-scores) in order to avoid biases arising from outliers (e.g., a participant that used an unusually wide range of numerical ratings).Although the absolute values of

he reporte
standardized scores are not meaningful, the relative values should reflect real differences experienced by the sample of participants.

Standardized ratings of urgency across the sound frequencies tested may be seen in Fig. 1.Urgency ratings were not equivalent across pulse rates, F ͑12,348͒ = 5.26, p Ͻ 0.0001.Trend analysis revealed that the linear trend was not significant, F ͑1,29͒ = 1.16, n.s. and the quadratic trend was only marginally significant, F ͑1,29͒ = 4.39, p Ͻ 0.05.The best-fitting polynomial trend was cubic, F ͑1,29͒ = 47.18,p Ͻ 0.0001, indicating that there are two

anges in the directiona
ity of the relationship between urgency and pulse rate (for the range of pulse rates tested).The strong cubic trend is a highly unusual scaling result and suggests the possibility of two underlying power functions.The first, peaking at 17.68 Hz, likely corresponds to the upper limit for which sequential pulses may be resolved (i.e., infrapitch).For higher pulse rates (e.g., beyond 35.36Hz), sequential pulses appear to fuse and give rise to a clear pitch percept (see also Fitzgerald and Wright, 2005;Miller and Taylor, 1948;Pollack, 1969).Intermediate pulse rates would have had a repetition rate that was too high to resolve independent pulses but too low to yield a clear pitch percept.These results strongly suggest that the experience of urgency in response to an auditory warning is mediated by perceptual constructs.

Following previous urgency research (Hellier et al. 1993;1999), urgency ratings were mapped using an application of Stevens Power Law (Stevens, 1975), Eq. ( 1):
U = kf m ͑1͒
where U is the judged urgency (in log units), f is the frequency or pulse rate (in log units), and k and m are the intercept and slope of the line (exponent) of best fit.

For the range of pulse rates from 3.13 to 17.68 Hz ("infrapitch region"), the power function exponent was 1.10.For the range of pulse rates between 35.36 and 200 Hz ("pitch region"), the exponent was 0.32.The relative and absolute value of these exponents are comparable to those reported by Hellier et al. (1999) for the warning parameters of speed and pitch.


Response time experiment

In order to verify whether the effects of the urgency mapping experiment reflected the experience of urgency, Experiment 2 asked partici ants to perform a tracking task (Makeig and Jolley, 1996) while occasionally responding to an auditory warning as quickly as possible.If the urgency ratings wer perienced urgency, there should be an inverse pattern of response times for the same stimuli.


Participants

Nine participants (six women and three males) with normal hearing were asked to participate in the tracking experiment.The mean age of participants was 22.8 ͑SD= 1.7 y͒.The procedures were approved by the Wilfrid Laurier University Research Ethics Board and all participants gave informed consent.


Stimuli and apparatus

The tracking task was presented on a PC computer with a standard video display and roller mouse using

OMPTRACK software (Makeig
and Jolley, 1995).The pulse-train stimuli and apparatus were identical to those described in Sec.2.2.


Procedure

The tracking task required participants to use a computer mouse to keep a circular cursor within a target circle by compensating for simulated buffeting and gravitational forces that acted upon it.Participants were asked to simultaneously listen for the auditory warning and to respond to i

as quickly as
possible whenever it was heard by pressing a button on a button box (i.e., not the mouse button).


Results and discussion

Standardized response times may be observed in Fig. 1.All participants displayed a high degree of vigilance in the tracking task.An ANOVA confirmed that response times varied wi

regard to pulse rate,
F ͑12, 96͒ = 2.27, p Ͻ 0.05.Average response times to pulse trains were shortest for pulse rates of 17 Hz ͑385.36 msec͒ and 200 Hz ͑384.14 msec͒.By comparison, response times were much longer for the lowest pulse rates in the infrapi

h region (
.13 Hz,524.17 msec;4.42 Hz,546.04 msec) as well as for the lowest pulse rates in the pitch region (35.36 Hz,435.46 msec;50 Hz,483.04 msec).It is important to note that these response time differences were obtained in a fully alert low-cognitive load condition.The response time differences would likely be further exaggerated under less optimal cognitive conditions.Nonetheless, the correlation between me

urgency ratings and me
n response times was negative and highly significant, r͑11͒ = −0.84,p Ͻ 0.0001, suggesting that the polynomial function obtained for urgency reflected the experience of urgency, rather than a conscious integration of discrete perceptual mappings.


Pitch strength scaling experiment

To verify the phenomenological descriptions of pitch regions described in Sec.2.4, pulse trains were subjected to a magnitude estimation task involving pitch strength; that is, the extent to which sounds give rise to a pitch percept.We expected perceived pitch strength to be at baseline (equal to pitch strength of white noise) between 17.68 and 35.36 Hz (transition region) and to rise sharply beyond 35.36Hz (pitch region).


Participants

Twenty-seven participants (21 women and 6 men) with normal hearing were asked to provide magnitude estimations.The mean age of participants was 19.13 years (SD 1.5 years).


Stimuli and apparatus

The stimuli and apparatus were identical to that described in Sec.2.2 with the exception that participants heard stimuli through Sennheiser HD 580 Precision headphones and the addition of a standard sound consisti

of 2.5 s broadband white noise pr
sented at 70 dB SPL.


Procedure

Participants judged pitch strength of each pulse train relative to the standard using a freemodulus magnitude estimation task.The following specific instructions were provided in order to clarify the objective of the task: "We have arbitrarily assigned the standard a pitch strength value of 10.You will be judging the pitch strength of the comparison sound in each presentation relative to the s

ndard.If the
omparison sound appears to be of the same pitch strength as the standard, then you would give a response of 10.If the comparison appears to have three times the pitch streng

of the standard, then
you would give a response of 30, and so on."In total, each participant judged all sounds four times each.Sessions lasted approximately 25 min.


Results and discussion

The mean standardized ratings of pitch strength varied across pulse rates, F ͑12,312͒ = 33.68,p Ͻ 0.000

Figure 2 s
ows that there was no change in pitch strength between 17.68 and 35.36 Hz (transition region).Pulse trains in this region had pitch strength that corresponded to that of an extended sample of white noise-i.e., pitch was ambiguous.There was a sharp rise beyond 35.36Hz, which is suggestive of a fusing of pulses leading to a tonal sensation with an increasingly clear pitch level with increasing pulse rate.Examination of Fig. 2 also reveals a drop off in pitch strength below 17.68 Hz (infrapitch region).The drop-off is somewhat unexpected given that pulse trains in this region do not appear to fuse and may reflect metacognitive awareness of the transition from infrapitch to pitch with increasing pulse rate.

These scaling results are consistent with mor

objective tests of low-
requency pitch perception (Pressnitzer et al., 2001;Russo et al., 2007) and with pitch matching experiments involving pulse trains (Miller and Taylor, 1948).The latter study showed that the frequency of interruption of a white-noise pattern only corresponded to the matched pitch of a pure tone for frequencies above 40 Hz. 1


Conclusions

The current study has identified two local maxima in a nonmonotonic (polynomial) function relating pulse rate to perceived urgency.The first maximum at 17.68 Hz corresponds to the positive correlation known to exist between speed and urgency (Guillaume et al., 2003;Hellier et al., 1993;1995;1999).Sounds in this region had very low pitch strength (i.e., infrapitch) consisting of a sequence of resolved pulses.The dip beyond 25 Hz likely reflects the transition from independent to fused pulses that is, a transition from a sensation involving high-speed and no pitch to a sensation involving no speed and clear pitch.The second maximum, at 200 Hz reflects the positive correlation known to exist between pitch and urgency (Guillaume et al., 2003;Hellier et al., 1993;1995;1999).These findings suggest that the influence of rate-based cues on the experience of urgency in auditory warnings is

ediated by p
rceptual constructs.

Fig. 1 .
1
Fig. 1.Mean standardized urgency ratings and mean standardized response times for each pulse rate.Error bars represent standard error.


Fig. 2 .
2
Fig. 2. Mean standardized pitch strength ratings for each pulse rate.Error bars represent standard error.

J. Acoust. Soc. Am. 122 ͑5͒, November 2007 © 2007 Acoustical Society of America EL185
J. Acoust. Soc. Am. 122 ͑5͒, November 2007 F. A. Russo and J. A. Jones: Perceived urgency EL187
J. Acoust. Soc. Am. 122 ͑5͒, November 2007 F. A. Russo and J. A. Jones: Perceived urgency EL189
AcknowledgmentsWe wish to thank Farina Pinnock for research assistance.Research was supported by Discovery grants awarded to each author from the Natural Science and Research Council of Canada and a Research Fellowship from Wilfrid Laurier University awarded to the second author.
. J. Acoust. Soc. Am. 1225November 2007

. F A Russo, J A Jones, Perceived urgen