Why is it that when we put our heads underwater in the bathtub, we hear the noises in our home better?

This may seem even stranger if we remember that sound passes from air to water, and vice versa, with great difficulty (a fact that also has important consequences for how the middle ear works, and for medical ultrasound).

Indeed, the impedance of air is only about three thousandths of that of water, which means that almost all the acoustic energy coming from one of the two media and striking the air-water interface is reflected, and not transmitted into the other medium.

Transmission is possible, instead, between the water and the solid walls of the tub. We can conclude that the sounds heard with our head underwater come from vibrations transmitted directly to the structures of the building. So thuds, footsteps and noises produced by impacts will be heard well, but conversations will not.

• On these topics see the pages impedance, impedance matching, refraction, refraction in one dimension (in Italian), and experiment with the 2D Waves app, for example following one of the guided tours on refraction.

A final note concerns the disorienting effect that sounds perceived in water (for example in the sea) can have. It depends partly on the fact that locating a sound source in space relies heavily on the brain measuring the difference between the arrival times of the sounds at the two ears. Now, in water the speed of sound is about four times higher than in air, and the time differences between the two ears become about four times smaller than those the brain is used to. Localisation therefore becomes much less precise, and often impossible. Sounds seem to come "from everywhere".

• On this last topic see the page on localisation of the sound source

Why is it that we seem to sing better in the shower?

In normal conditions the sound we emit reaches our auditory system both by bone conduction and through the air: the sound coming out of the mouth goes around the head and reaches the ears. Outdoors, however, almost no sound comes back to us reflected from the surroundings. The walls of the shower cubicle obviously increase the amount of reflected energy that reaches our eardrum. Because of the small size of the cubicle, they reflect particularly efficiently waves whose frequencies are close to those of singing, leading to the formation of standing waves which, on reaching our eardrum, reinforce the sound wave originally emitted. If you want to find out more about how the size of a room selects the frequencies of standing waves, visit the pages architectural acoustics and interference between reflected waves.

Is it true that if we place our ear on a train track, we will hear the approaching train sooner than if we were to hear it in the air?

This is a somewhat dated, though correct, example used to show that the speed of sound in solids is much higher than the speed of sound in air.

An example of this kind seems particularly suited to the newly settled Wild West, where endless railway lines, travelled by slow and very rare trains, stretched across boundless, silent spaces. If we consider, however, that trains at that time ran on coal and left a conspicuous trail of smoke, putting your ear to the track may not have been the quickest way to notice an approaching train.

Nowadays, considering that train traffic is incomparably denser and more frequent, that many tracks run through urban or otherwise relatively noisy areas, and that every crossing has a level-crossing light and sound signal, it does not seem advisable to use this technique to convince yourself that it works.

• See instead the pages on the speed of mechanical waves, the speed of sound, and the speed of sound in different media.

I’ve seen perforated panels hanging in some concert halls. What purpose do they serve?

They serve to modify the absorption characteristics of the walls, that is, the ratio between the fraction of energy reaching the walls and the fraction they absorb. As explained on the page on architectural acoustics, the acoustic characteristics of a hall can be partly modified (depending on the type of music performed) by changing some of its movable furnishings (curtains, movable panels, added rugs, carpeting, etc.). The geometry of the movable furnishings (for example the presence of holes) is designed for the selective absorption of certain frequencies.

Can outside noise make a window pane vibrate? And does double glazing help?

Yes, in fact this is exactly how noise gets in: the sound wave exerts a varying pressure on the glass, which starts vibrating and in turn radiates sound into the room. A real noise contains many frequencies: the glass vibrates most strongly at those close to its natural frequencies (see resonance).

• Single glazing. The heavier the glass, the less it lets itself be set vibrating: insulation increases by about 6 dB for every doubling of the mass per unit area or of the frequency (the "mass law"). The exception is a band of frequencies, around a few thousand Hz for common glass, in which the bending waves of the glass "follow" the sound wave and insulation worsens (coincidence effect).
• Double glazing. The outer pane, vibrating, sets the air in the gap vibrating, which in turn sets the inner pane vibrating. The two panes and the air between them form a mass-spring-mass system with its own resonance frequency, which for common double glazing (two 4 mm panes and a 12 mm air gap) lies around 250 Hz: there the insulation is worse than that of a single pane of the same weight. Above that frequency double glazing insulates much better. It works better with wide gaps and panes of different thickness, so that their resonances do not coincide.
• Even when there is no air (vacuum glazing) the vibration can pass through the frame and the wall, so construction details matter as much as the glass.

Low frequencies, such as the rumble of engines, compressors or steam plants, are the hardest to stop with any kind of glazing.

Why does an echo repeat only the last syllable of a word?

When a sound overlaps with a delayed copy of itself, the two are perceived as distinct sounds only if the delay exceeds a certain threshold. The threshold depends on the type of sound: for the syllables of speech it is of the order of a tenth of a second. Reflections arriving earlier merge with the direct sound: they change its timbre and reinforce it (this is what happens in every room), but they do not form an echo. Since in a tenth of a second sound travels about 34 m, to hear an echo the reflecting wall must be at least about 17 m away (there and back).

Only the last syllable is heard because the echoes of the preceding syllables arrive while one is still speaking. For example, saying "casa" in front of a distant wall, the echo of "ca" returns while one is pronouncing "sa": the direct voice, which comes from closer and is much louder, covers it (masking). The echo of "sa" instead arrives when one has stopped speaking, so it is heard clearly. If the wall is very far away the whole word can be heard repeated.

Do noise barriers with a rounded or shaped top edge reduce diffraction?

A little, but they do not eliminate it. A barrier works because sound, to reach someone behind it, must diffract around its top edge. The attenuation depends mainly on the difference δ between the path passing over the edge and the direct path, compared with the wavelength λ. A widely used empirical formula (due to Maekawa) gives an attenuation of about

${\displaystyle \mathrm{\Delta }L\approx 10{\log }_{10}(3+20N)\mathrm{d}\mathrm{B},N=\frac{2\delta }{\lambda }}$

For example, with δ = 0.5 m at 500 Hz (λ ≈ 0.68 m) about 15 dB is obtained. Low frequencies, with long wavelengths, are attenuated less: this is why a barrier counts mainly for its height.

Shaped edges (T- or Y-shaped, with cylinders or with sound-absorbing elements) create multiple diffraction or absorb part of the sound near the edge. Compared with a simple barrier of the same height they generally gain a few decibels (often between 1 and 3 dB, depending on the shape and the frequency), roughly as if the barrier were a little higher. There is nothing magic in the rounded shape itself: what matters is how the edge changes the paths and how much sound it absorbs.