Wikipedia:Reference desk/Archives/Science/2023 February 12

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February 12

What waveform sounds loudest to the average human?

I wish to create a sound file to make the loudest alarm possible on my phone. Assuming I have complete control over the audio waveform, for a given volume setting, what is the most perceptible waveform? Could it be a square wave of maximum amplitude at 3700 Hz, alternating with complete silence at around 2 Hz? Thanks, cmɢʟee⎆τaʟκ 12:35, 12 February 2023 (UTC) cmɢʟee⎆τaʟκ 12:35, 12 February 2023 (UTC)

If you folow the people who make adverts you'd first start with a low sound from the film that catches your attention and you strain to hear and theN BAM!! THEY GET YOU! ;-) Seriously ambulances and ads are your best bet I think. NadVolum (talk) 12:50, 12 February 2023 (UTC) >

There must be more to it than the most perceptible frequencies. Square waves have many harmonics, so they cover many frequencies at once, which possibly helps. You describe a psychological effect which lures a person into listening, and that is no doubt exploited in music to make loud passages seem louder, though it might not work subliminally (for an alarm). Consider also percussive effects rather than periodic waveforms:  Card Zero  (talk) 13:25, 12 February 2023 (UTC)

A square wave has no even components; this is what gives certain woodwinds their quacking quality. A sawtooth wave includes all overtones. —Tamfang (talk) 19:07, 18 February 2023 (UTC)

From the graph shown at the article Loudness we can see that the (subjective) loudness given a sinus wave of a fixed sound pressure level is loudest at about 3185 Hz. So the range around 3000 to 3300 Hz should be well represented in the waveform's spectrum. However, an individual may be hearing-impaired in just that range. Audible alarm signals as produced by alarm devices generally have a time-varying main frequency, which not only solves the problem of such partially hearing-impaired individuals, but also has a better effect of drawing one's attention than an unvarying signal. Next to changing the frequency, it is also common to use a varying loudness. I don't recall the details, but I once produced alarming sounds by sending the lower n bits of the series of the squares of the integers (0, 1, 4, 9, 16, 25, ...) to a D2A converter coupled to a loudspeaker. I vaguely remember XOR-ing the bit patterns also with slowly varying other bit patterns.  --Lambiam 13:58, 12 February 2023 (UTC)

Some information at Siren (alarm) may be useful, particularly under 'Physics of the sound' and 'Best practices'. If it is just for you, try getting a hearing test and aiming at the frequencies where you have most acute hearing. Alternatively, if the requirement is to be heard in a noisy environment, get a frequency scan of the noise and aim your alarm at the gaps. -- Verbarson  ^talk_edits 17:33, 12 February 2023 (UTC)

Crazy Frog is perhaps the most annoying ringtone, even at low volumes, which may serve your purpose. MinorProphet (talk) 19:45, 12 February 2023 (UTC)

Another aspect is that you may wish to localise the sound. A high pitched sine wave is not good for that, but if you modulate it, or include lower pitched sound, you can then tell which direction the sound comes from. This is because the autocorrelation of the waveform has to have a significant value, for the difference in time that the sound arrives at different ears. Other things to consider are how efficiently the phone speaker can produce sound, and there will be considerable distortion introduced due to mechanical aspects and shape of the phone. So really you would probably have to measure the sound output experimentally by listening. Graeme Bartlett (talk) 22:36, 12 February 2023 (UTC)

Perhaps I'm misunderstanding, but our article Sound localization seems to say the opposite: As the frequency drops below 80 Hz it becomes difficult or impossible to use either time difference or level difference to determine a sound's lateral source. That's why when positioning stereo speakers, the position of the subwoofer is not very important; our article says Frequencies which are sufficiently low are not easily localized by humans, hence many stereo and multichannel audio systems feature only one subwoofer channel and a single subwoofer can be placed off-center without affecting the perceived sound stage, since the sound that it produces will be difficult to localize. CodeTalker (talk) 17:58, 13 February 2023 (UTC)

It also says "For frequencies above 1600 Hz the dimensions of the head are greater than the length of the sound waves. An unambiguous determination of the input direction based on interaural phase alone is not possible at these frequencies." (bold mine). It goes on to describe how localization can be done using other characteristics of the sound, in general localization is difficult for sounds which are outside of the 80-1600 Hz range both above and below. A pure sine wave at 3000 Hz can be difficult to localize. --Jayron32 18:32, 13 February 2023 (UTC)

You should take into account that any square waveform expands into Fourier series. So, for your example with 3700 Hz you will also hear harmonics with frequencies 7400, 11100, ... Hz. Ruslik_Zero 20:28, 13 February 2023 (UTC)

Both of us have said this (I didn't mention the fourier series, but I had it in mind when mentioning the harmonics of square waves). But I wonder whether hearing really does concern itself with sine waves, or whether (in a corresponding way to the retina detecting edges) it recognises some higher-order structures? Certainly a square wave seems to me to have one frequency - it doesn't sound like a chord, but like a buzzing note. I looked at Neural encoding of sound, in particular the last sentence, The cortex seems to perform a more complex processing than spectral analysis or even spectro-temporal analysis, and its associated reference. Probably this question is unresolved. But our brains are eager to recognise faces (evergreen ref desk link to pareidolia), so there might be a corresponding tendency for auditory perception to be alert to the sounds of important things. Sounds that correspond to real-world objects rattling, colliding, or breaking, perhaps, or animal sounds, or footfalls.  Card Zero  (talk) 19:44, 15 February 2023 (UTC)

The cochlea responds to higher frequencies at the outer end, and lower frequencies further in, due to the varying stiffness of the hair cells. Therefore there is a physical decoding of the sound into a spectrum of frequencies even before the brain gets the signal. How closely this corresponds to some sort of Fourier analysis I do not know. See also Tonotopy. -- Verbarson  ^talk_edits 20:35, 15 February 2023 (UTC)

XY problem: Going out on a limb, I'm assuming the actual problem is "I sleep through alarms". Maybe you could try going to bed earlier? Though, depending on chronotype this can be a real issue, in which case you might want to think about how possible it woule be to restructure your life so you don't have such an issue with "getting up" fighting your body's circadian rhythms. There are all manner of things, like "light alarm clocks", that use things other than/in addition to sound. (Alarm clock could use some content about them added.) If you have real problems with excessive daytime sleepiness that don't seem to get better even when you get ample hours of sleep, you ought to seek medical attention. Ask me how I know. --47.147.118.55 (talk) 10:25, 15 February 2023 (UTC)

References

Thank you so much for all the fantastic analysis and recommendations. I should be able to wake up now! cmɢʟee⎆τaʟκ 02:06, 16 February 2023 (UTC)