Hi, Philip,

This looks like an interesting experimental question. However, just thinking about it, temperature seems to be the ultimate confound. First, I don't think it would be possible to isolate the listener from the thermal difference between conditions while retaining the effect of temperature. If the listener is kept, say, in a warm room, any differences between conditions would be abolished by the time the sound arrives at the ear. On the other hand, if you expose the listener to different temperatures, the auditory system (and everything else) would be affected in ways that preclude meaningful measurement of the difference. Perhaps, there is a way forward but thinking about would have to wait until things are back to normal. I hope this helps. Happy New Year and all the best,

Alex

Frequency is a measure of the number of pulses arriving at the ear within one second (time). Wavelength is the distance (space) between two of those pulses. Frequency is thus determined from the wavelength (and can be calculated), and the reverse is true for wavelength which can be determined if you know the frequency. However, a sound produced at, say, 1 kHz (one thousand pulses per second) does not necessarily arrive at the ear at 1 kHz (ref. a moving object/sound and the Doppler effect). This and other issues can affect the perception of pitch of a sound. Hope that helps, Peta

Sensors in the inner ear (hair cells) percieve only vibrations, i.e. frequency of sound (in technical terms) - whatever origin these vibrations are: Tuning fork, Doppler shifted sound, underwater sound (much larger wavelength than in air!!), hot or cold air, etc. etc.)

vm

The ear analyzes frequency and is insensitive to wavelength. 1 kHz will sound like 1 kHz in winter and in summer. For space, interaural time differences are being translated to azimuthal location. The temporal precision is impressively high (JND of 50 microseconds for humans under optimal conditions), but still a change of 10% because of changes in temperature in this map would be to all practical purposes undetectable.

The number of periods generated in a certain interval of time is completely determined by the sound source. If we perceive a different frequency, as in the Doppler phenomenon, this is caused by the change of the distance between source and ear. If we hear a higher frequency, for example, all these extra periods within the same interval of time come from the decreasing distance. In a way we 'use' the extra waves that exist between source and ear by moving towards the source. Where else would these extra periods come from? If we don't alter the distance there cannot be more periods than the source generates in a certain time. For lower perceived frequencies it is the other way around. In other words: we don't perceive pitch from wavelength. The wavelength is only a distance in the sound path. (In the cochlea, one could argue, there must be a wavelength in the fluid but the dimensions are so small that only a small fraction of a wavelength fits in the cochlea. The auditory nerves are capable to detect where in the cochlea the resonations take place and the position depends on the frequency. To detect frequency, at least a couple of sound periods are needed. Anyway, the circumstances in the cochlea remain unaltered and are independent of the temperature in the room.)

Frequency and wavelength are inversely related to each other. Higher the frequency, shorter the wavelength and vice versa. Velocity of sound in a medium (air, e.g.) is the velocity of pressure wave travelling spherically (in 3-D) in that medium and depends on type (composition) of medium (air), gas constant R, its absolute temperature T and ratio of specific heats Cp to Cv. Higher the temperature, higher the velocity of sound, lower the temperature, lower the velocity of sound. That is why in the night background noise is suppressed due to lower velocity of sound. That is how engineers understand sound. This basic science of sound is applied by aerospace engineers to design high speed flow of gases in constant area pipes, varying area nozzles / diffusers and study the effects of high speed movement of solid objects (aircrafts, rockets, projectiles, meteorites) in still air.

hi philip,

as you said the coding is only frequency dependent for one ear but the smaller wavelength should enhance the localisation of the source in binaural configuration, the phase shift between ears increasing when the wavelength decrease.

Hope it helps

Hey, I am actually finding it quite difficult to understand this question. Does "calibrating the object to vibrate at 1000 cycles per second" mean that the source is vibrating at 1000Hz or that the resulting sound wave a frequency of 1000Hz.

What I can understand is that the source seems to be vibrating at 1000Hz but the resultant sound wave's wavelength as well as frequency are different from the source. The sound wave incident on the listener's ear does not have has its wavelength corresponding to its frequency.

So the listener perceives frequency of the incident sound wave and he can also perceive the frequency and also indirectly the frequency.

(The incident sound always has frequency corresponding to its wavelength)

P.S : The human ear responds to only the rarefaction phase of the sound.

Simple example: Just set up a standing wave in a room and move around in the room, Then, the pitch will (basically) remain but you will experience (a quarter of ) the wavelength in terms of the distance you need for moving your ear(s) from a node to an antinode of the standing wave. Happy new year!

Hi Philip and Happy New Year!

About your question, you calculated the frequencies using a sound velocity of 343m/s but you used the wavelength calculated for two different conditions (and different sound velocities). Therefore, you obtain two different frequencies but that is wrong since the wavelength is a function of the source frequency and the sound velocity for each case ( the sound velocity is constant only if the characteristics of the medium across which the wave propagates remain constant). The vibration of the tymphanic membrane will be again 1000 cycles per seconds in both cases. After the transmission of the vibration from the tymphanic membrane to the oval window in the cochlea, the conditions for sound transmission are different than outside the ear and more stable. When saying that the auditory system perceives the wavelength, we are meaning that is the wavelength of the oscillation of the basilar membrane and this oscillation is proportional to the vibration of the tymphanic membrane and independent of the changes in speed of propagation of the sound waves outside the ear. Since the conditions of the medium inside the cochlea are stable, the wavelength is proportional to the frequency always in the same manner, so talking about wavelength or about frequency is the same. Thus, I will say that if we perceive any difference (assuming free-field conditions) is because there is a change if the transmission from the tymphanic membrane to the cochlea (relaxation or constrain of the muscles around the ear) but not because the sound is propagating with different velocity. If is inside a room then you should take into account standing wave as Johan explained before.

I hope this helps!

Javier, Happy New Year to you too. The frequencies were just an example of how different these two wavelengths are: not much, but noticeable if they were different frequencies. I'm glad this question has elicited such an active conversation. Cheers.

Just my guess:

The hearing curves show a peak sensitivity around 3500 -4000 Hz. This is associated with the resonance of the auditory canal. This (first) resonance occurs for frequencies corresponding to waves with a wave length of about 4 times the canal length, which is about 2.5 cm. So if you change the temperature of the air inside the auditory canal, the resonance frequency will change (because the wavelength remains the same but the soundspeed not) and this peak sensitivity in the hearing curve will change. This should be sensible. Otherwise the evolutionary adaptation of our hearing system to match the typical human voice frequencies would not have been possible.

The sound source produces, in this example, 1000 periods per second, no more, no less, independent of the medium. The medium can only have influence on the propagation speed and as a consequence the wavelength, which is only a part of the distance between source and ear, depends on the medium as well. At the receiver side the eardrum vibrates according to the water (or air) pressure vibrations. The time of one period remains constant 1 ms. If you would hear, for example, a higher tone, where would all these extra periods come from? Not from the source, not from some 'memory' in the medium and not from alterations of the distance between source and eardrum (as would be the case of the Doppler effect). The only things that are dependent of the medium are the delay (which is a constant and which doesn't alter the frequency) and the spatial perception (which is a reverberation effect and also doesn't influence the frequency). So from the eardrum vibrations to the auditory nerves at the basilar membrane everything remains the same (even the temperature remains constant, so even the wavelength within the auditory system will not be dependent of the medium outside the ear). The time of one period remains exactly 1 ms in all circumstances because nothing produces extra periods within a certain time interval and nothing 'eats' periods. The tone will be exactly 1000Hz, in air and in water. You can test it with an (underwater) speaker and microphone if you like.

Correction:I mixed up two different questions here. Instead of air and water, read: hot air and cold air, please.

Ton, your points are valid. But with two ears, pitch is not the only way to detect wavelength. The heart of the question is whether the non-pitch factors, like interaural phase/time differences, or more specifically the changed relationship between frequency and interaural phase/time differences are noticeable. In this case I estimated a 15cm interaural path length difference would translate to about 24microseconds difference in ITDs at the two temperatures, which equates to about 3 deg. in lateralization difference. This is very near the frontal minimum audible angle, and well below the side MAA, so probably negligible as the majority of responses have determined.

A post scriptum to my answer above: it goes without saying that changing the air temperature inside the auditory canal will be difficult, if not impossible, in other than laboratory conditions.

Philip, you're right about the phase/time differences. That means that the spatial perception can be influenced by the air temp. due to the speed differences at different temperatures. But the phase differences (or time delay differences which is basically the same) between the vibrations of the two ear drums give direction info only. Not alteration of the frequency. (I categorized this phase info under the reverberation effects.) The phase differences do not alter the frequency. The frequency of the eardrum signals cannot be different from the frequency of the source: the number of periods within a certain time interval cannot be altered by the propagation speed. The air can be seen as a linear filter which cannot change the input frequency. It is completely defined by the source frequency independent of the time delay in the medium.

A second point is that the wavelength is no feature that the auditory system detects. It detects only frequency by determination of the position of the center of the vibration on the basilar membrane. The wavelength could only be detected by simultaneously firing of nerves at different positions and nerves almost never will fire at the same moment and especially not with length precisions of a couple of microns. (A full wavelength of a 1000 Hz tone in the cochlear fluid would be about 1500cm whereas the length of the complete cochlea is only about 4 cm.)

And the third point: even if in some hypothetical thought the differences of such tiny parts of the very long wavelength in the cochlea could be detected by the auditory nerves, the different air temperatures outside the ears will not have any influence on the cochlea because the frequency at the eardrums remains exactly 1000 Hz.

Hope I could explain things in an understandable way, otherwise, or if you disagree, please say so.

A comment to Sjoerd Rienstra above. It may be difficult to change the temperature in the auditory canal but it should be easy to change the speed of sound by deluting the air inside the canal with Heiium, which would increase the wave length. The frequency would still be the same but the resonance frequency of the ear and its frequency response curve would change. But coming back to the original question: "can the human ear distinguish wave lengths independently from frequency", the answer would still be no.

Sorry for the delay of my answer, I am just back from winter vacations in Italy. That was so nice!

Reading your question, I realize that our problems depend a lot on our background. We, Philip and I, consider phenomena from different side of the tympanic membrane. Let me tell you what is going on inside the cochlea. There are several transduction mechanisms before perceiving a tone and the last one is physiological. There are an ‘electrical’ motor (fast active phenomenon) and a low feedback loop which adjusts the vibration of the organ of Corti with efferent fibers to enhance the efficiency of the discrimination process. And this is not that simple because these phenomena concern only the medial-basal cochlea (up to 1000 Hz). The frequency discrimination process is different for the apical cochlea dedicated to low-frequency discrimination. The latter is called passive phenomenon “phase locking”.

As you can read, the frequency discrimination process depends on the frequency and unfortunately 1000Hz is just at the frontier between the two cochleae (the basal and apical cochleae). In my opinion, a little difference in terms of frequency or wavelength does not matter for the frequency sensation. The auditory receptor and the auditory nervous centers will adjust the sensation much more than the tiny difference of wavelength.

Happy New Year .

I read the answer from Pierre and I felt the urge to react. The auditory system is quite complicated w.r.t. the frequency detection, I agree. However, for regarding the difference between the two listening circumstances, i.e. the hot and the cold air, we can bring the question back to the two different vibration signals at the eardrums, because, from these signal positions on, the complete auditory system is the same, independent of the air temperature of the room.

For each eardrum separately, the vibration has exactly the same frequency as the source, in this case 1000Hz, no matter the amount of delay of the waves from source to eardrum. There cannot be a different frequency like I argued before. And here is no question of wavelength (how could one eardrum detect the wavelength if it is positioned in one spot only?). So the only thing we have to focus on is the phase delay between the eardrum signals and the perception of it. For continuous tones a (constant) phase difference has no influence on the frequency perception (the auditory nerves react on the signal variations as they occur in time which is determined by the signal, not by the system). The phase difference only can give spacial information (the direction of the source in the room and the reverberation properties). This phase difference remains constant as long as the positions of source and ears do not vary. At each temperature the phase difference can have different values but as long as the temperature in each listening circumstance remains the same, the phase difference remains the same too.

So these phase differences can be perceived, not the frequency. The answer to the question "Can we hear the difference between the same tone in a cold space and a hot space?" in my opinion therefore must be: "No, only the spatial impression can be different, not the frequency".