# Amplitude of a crest and trough in a sound wave?

Lets say we have a sound wave, it has a frequency, wavelength, crest, trough, etc.

My question is, is the crest of a sound wave equaled to high amplitude/ high volume and if so, does that mean the trough is low amplitude/ low volume?

I'm basically trying to figure out if the crest and troughs in a wave represent maximum volume at the crest peak and maximum silence at the troughs peak.

A crest and a trough both cause the eardrum to move away from its normal, undisturbed, resting position. Hence, the crest and the trough both embody a loud sound. When there is no sound, the ear drum is still; it is resting in a central position. When sound waves strike the eardrum, it moves the eardrum inward (crest) and outward (trough). The ear converts the inward motion and the outward motion into electrical impulses, which are sent to the brain.

The loudness of the sound depends on how far the eardrum is moved/displaced from its resting central position. Hence, a really tall crest would be associated with a loud sound, but a really deep trough would also be associated with a loud sound. Zero sound would be embodied by a flat line that does not disturb the eardrum at all and doesn't move the eardrum away from its normal, central, resting position.

We can also look at this mathematically. The loudness or volume that we hear depends on the intensity of the wave. Intensity is acquired by squaring the amplitude/maximum displacement. Hence, when we take the square of a negative number, the resulting intensity value becomes positive.

Caveats:

• Most sound waves vibrate the eardrum at least ~100 times per second, which is extremely fast. We can't distinguish a single crest from a single trough, and a lot of averaging occurs in the process of hearing. In music, the tones we hear do not change at this same frequency; they change much more slowly than 100 times every second. Hence, it's more useful to talk more about the amplitude of these prolonged waves rather than pointing to a single crest or a single trough, which we can't distinguish anyway.

• Sound waves are actually longitudinal. That is, they form rarefactions and compressions in the air, not crests and troughs.

• Loudness is subjective and roughly follows the log of the relative sound intensity.

• The anatomy of the ear is complex, and the electrical signals are generated by the movement of hair cells in the cochlea. Some hair cells respond to higher frequencies, and others respond to lower frequencies, etc.

• Whether the crest moves the eardrum inward or outward is totally arbitrary and depends on the perspective and coordinate system we're using to measure the eardrum's displacement.

• Thanks so much for your stupendous reply @jdjazz! Would say then that although in a transverse wave graph with crests and troughs, the two are opposite sides, sonically they are the same thing? Or what is the reason they are opposite of each other on a transverse graph? Thank you again! Commented Jun 14, 2019 at 1:14
• The air molecules look like this as they carry a sound wave through your ear canal. Each dot is a molecule of air. If we watch a single air molecule (for example, one that has been highlighted in red), we see that each molecule vibrates left and right, back and forth. When the molecule moves to the left of its center position, the wave shape dips down to a trough. When the molecule moves to the right of its center position, the wave rises up to a crest. The rightward & leftward movements are both passed on to the eardrum. Commented Jun 14, 2019 at 13:27
• But when it comes to volume (i.e., loudness), the ear doesn't distinguish between leftward movement of the eardrum and rightward movement of the eardrum. The loudness simply depends on (the square of) how far the ear drum moves from its central, resting position. Commented Jun 14, 2019 at 13:31

is the crest of a sound wave equaled to high amplitude/ high volume and if so, does that mean the trough is low amplitude/ low volume?

Not exactly. A sound wave is something that is perceived when sound pressure is changing at a rapid frequency - oscillating up and down at 20 cycles per second or more.

If we say that the crests are high pressure and the troughs are low pressure, You get a loud sound when the difference between the crests and troughs is big. You get a quiet sound when the difference between the crests and troughs is small.

If you look at those two areas of the picture, the peaks and troughs are further from zero in the high volume (loud) area than the low volume (quiet) area. However, even in the high volume area, the oscillation frequently passes through zero. So seeing a low amplitude point on a sound wave doesn't necessarily mean that the sound is quiet, because the perceived volume depends how strongly the wave is oscillating.

• Great answer. You were helpful in helping me understand the larger the distance of a crest and trough the louder the amplitude. Thank you. Commented Jun 8, 2019 at 23:48
• Just been busy jdjazz and have yet to thoroughly examine the other two answers. Will do very soon if I find yours to be most helpful. Commented Jun 12, 2019 at 0:23

The quiet point in a sound wave is actually at the median point between the "crest" and the "valley" in a balanced wave, where the valley is equal in loudness to the crest but 180 degrees out of phase. That's as simple as I can explain it.

• Thank you very much. Can you detail what effect the 180 in phase has on sound? Is it purely a mechanism to create constructive and destructive interference or has it any other purpose? Commented Jun 14, 2019 at 1:16
• @Seery- The most important thing to understand first is that the silent part of the sound wave is at the median point between the crest and valley. Although the valley is 180 out of phase with the crest, there is the actual time difference between when the crest occurs and when the valley occurs. This eliminates any destructive action that might occur if both the crest and valley were to occur at the same instant. Commented Jun 14, 2019 at 14:06