Intuition for Sound Waves

Question

I recently started reading about the topic "Waves" and started learning it from Transverse Waves. After building enough intuition I moved on to longitudinal waves especially sound waves. While reading the same from "The Concepts of Physics-by H. C Verma", I came across the following part:

The fact that displacement is 0 where the pressure change is maximum and vice versa puts the 2 descriptions on different footings. The human ear or an electronic detector responds to the change in pressure and not to the displacement in a straight forward way.

Further more the author quoted and example of 2 loud speakers facing each other and a detector at the midpoint. The displacement of the particle at the detector is 0, however the pressure increases simultaneously in both directions. The detector would sense the pressure change and detect sound, though displacement of the particles is zero.

I could vaguely understand it, but could not form a solid idea about the same. A longitudinal wave is just the movement of particles about their mean (in the direction of wave propagation). However I couldn't intuitively think how a wave could possibly exist without the movement of particles at that point. Like in case of a standing Transverse wave, I could touch a node and not sense waves at work. But I cannot form a solid idea of why a detector could sense a wave without a wave existing in the first place at that point? Please tell me for some clarifications as I am rather confused about it myself.

Answer 1

Your textbook doesn't seem very understandable! This might help:

First, sound waves in air consist of small amounts of back-and-forth air movement accompanied by a small amount of rising-and-falling air pressure. The characteristics of air (its mass per unit volume and its elasticity) cause a pressure change to result in air movement, and air movement to produce a pressure change, in a way which makes the movement/pressure disturbance to propagate through the air as a sound wave with a certain characteristic speed.

When a sound wave in air hits a detector or an ear or some solid object, the energy being carried in the wave "piles up" against that object and as it does so, the wave itself comes to a halt and exerts pressure against that object. In that very instant, it could be said that the sound wave "doesn't exist" but this is not true: its forward motion has been converted into a rise in pressure.

Now an instant later, that pressure buildup pushes the nearby air back away from the object and the wave reforms itself, going now in the opposite direction: it has been reflected.

Most common sound detectors (including the ear) are transducers that convert air pressure changes into voltage changes. The amount of actual air motion involved in sensing the pressure changes is extremely small and some microphones (called pressure zone microphones) are deliberately designed to use the pressure buildup right next to an object to sense the incoming wave.

There are many excellent animations of longitudinal wave propagation on the web and I think watching them would also be of help. If you can, look for a different textbook on acoustics- one with the author name Beranek in it would be particularly good.

Answer 2

Let's consider a "light detector" first. A photo detector measures the light intensity, which is proportional to the square of the electric field, $I \propto |E|^2$. Therefore, if the electric field is maximal, we obtain a "large" signal and if at its minimum, we obtain a "small" signal.

Now, let's consider a sound detector. If we are standing on a "high mountain" our ears are subjected to a "low" air pressure. In contrast, if we dive under water, the pressure on our ears is "larger" than 1bar. Nevertheless, in neither case we hear a sound. Therefore, we conclude that our ears are not detecting pressure itself. Instead, our ears detect the change of pressure.

I'm certainly not an expert on the working principle of our ears, however, here is how I imagine it works:

• The frequency of the pressure variation (=change of pressure with time) is responsible for the tone we are hearing. If the frequency is "fast", the tone is high. If the frequency is "slow" the tone is deep. I reckon that the eardrum starts vibrating in a certain pattern, which depends on the frequency of the tone.
• In contrast, the amplitude of the eardrum vibration is responsible for the loudness of the tone. Therefore, if the pressure is given by $$ P(t) = P_0 + P_1 \sin(\omega t) $$ the constant offset $P_0$ is irrelevant for the "loudness". All what matters is the amplitude $P_1$ of the time varying term.

I don't comment on your last paragraph, because I reckon that it is merely the result of the above mentioned conceptional misunderstanding.