Understanding Pitch and Loudness in Sound Waves
To begin our discussion, we will consider the attributes or characteristics of any kind of wave. The most noticeable aspect of a wave is that it repeats in time. Whether it is a vibrating string on a violin or waves breaking at the shore, something is repeating.
Musical notes or tones have a pitch. The pitch of a particular note is often given as a number. For example, the note "A" in the middle of a piano is designated A=440. Now, the question is 440 what? A vibrating string on a musical instrument will vibrate or oscillate back and forth and will have a certain pitch. Since frequency always refers to some number of oscillations, we do not have to keep writing "oscillations" all of the time, so a shorthand has been developed.
Each way of writing this gets progressively more compact. Also, "per second" is more easily written as /second, and second is abbreviated as sec. What may be more unfamiliar is the designation that "/sec" = "Hz". Hz is an abbreviation of the unit Hertz, named after the physicists Heinrich Hertz.
Once we understand the meaning of a pitch or frequency of 440 Hz, we can ask a related question: how long does 1 oscillation of the vibrating string take? If the string oscillates 440 times in 1 second, then each oscillation will take (1/440) seconds. Another way to look at this is the following: if each oscillation takes (1/440) seconds then 440 oscillations will take 1 second. Again, we have used some shorthand notation. If the period is rather small, we don't want to keep writing lots of zeros after the decimal point, so we use scientific notation, instead. 10-3 seconds corresponds to 1 millisecond and 1 millisecond is abbreviated as 1 msec.
Repetitive sounds can be formed in different ways. Common, of course, is from a musical instrument. The individual echoes of the drum off each step are delayed from one another. So, to the drummer the echoes form a repetitive sound which then is heard as a pitch.
Besides the pitch of a musical note, perhaps the most noticeable feature is how loud the note is. The loudness of a sound wave is determined from its amplitude. While loudness is only associated with sound waves, all types of waves have an amplitude. Waves on a calm ocean may be less than 1 foot high. Good surfing waves might be 10 feet or more in amplitude.
Figure 1: A simple waveform with measurements included.
Frequency and Amplitude
The frequency of a sound wave is a measurement of how quickly the individual waves are following one another. This measurement is usually expressed using the SI unit Hertz (Hz). 1 Hz is equivalent to one wave per second.
The amplitude of a sound wave is a measurement of how intense the wave is. It is often helpful to visualize sound waves using a graph called a waveform. In this graph, the horizontal axis represents time, and the vertical axis can be understood as the position of a single particle in relation to its resting position.
When two or more sounds happen simultaneously, their sound waves combine, so what reaches our ears is a single, complex sound wave.
Figure 2: Two waveforms which reinforce one another.
If two sound waves are identical but offset by half a cycle - so one waveform peaks when the other bottoms out - the frequencies will cancel each other out, resulting in silence. If the frequencies of two sound waves are slightly different, the combined sound wave will alternate between periods of reinforcement and periods of cancellation, producing pulsing beats of sound which slow as the frequencies get closer.
Humans can generally hear frequencies from around 20 Hz to around 20,000 Hz, and can hear differences in frequency of about 3.6 Hz, meaning that humans are capable of discerning over 5,000 discrete pitches.
Musical Pitch and Tone Quality
Musical pitch is a continuous scale: given any two frequencies, there are an infinite number of different frequencies between them. Because listeners are usually unable to hear infinitesimally small differences - humans are typically capable of hearing frequency changes as small as 1 Hz - most musical systems make use of a discrete set of pitches. Most musicians hear frequencies at octave apart as being so consonant with one another as having a shared identity.
Most musicians train themselves to recognize the intervals between two different pitches. With this capability, given a named reference pitch, one can identify any other pitch by hearing the interval between them. Some people are able to identify pitches independently, without a reference pitch, a capability called absolute pitch or perfect pitch.
Figure 3: American singer Whitney Houston performing in New York City in 2009.
Most musicians train themselves to fluently identify the interval between two notes, a capability called relative pitch.
Although a wave repeats in time, its motion during on oscillation can be simple or highly complex. In fact, their amplitudes are also the same. Thus, if these two waves represented sound waves, the pitch and loudness would be the same in both cases. But would they sound exactly the same? The answer is No, because there is one more attribute to sound waves that you are familiar with, and that is tone quality. This is what makes different instruments sound different. A violin and a trumpet can play the same pitch with the same loudness, but we can easily tell them apart, because they have a different tone quality. In fact, the same instrument can create different tone qualities. If you pluck a guitar in different ways, you can get quite different tones. Try it! The technical musical term for this is timbre.
A foghorn located adjacent to the Sumburgh Head lighthouse in the Shetland Islands of Scotland.
Key Differences Between Pitch and Loudness
Here's a table summarizing the key differences between pitch and loudness:
| Feature | Pitch | Loudness |
|---|---|---|
| Definition | Pitch is how high or low a sound seems to us. | Loudness is how strong or soft a sound seems to us. |
| Depends on | Frequency of the sound wave (measured in Hertz, Hz). | Amplitude of the sound wave (measured in decibels, dB). |
| High/Low | High frequency gives a high pitch (like a whistle); low frequency gives a low pitch (like a drum). | Large amplitude makes a sound loud (like shouting); small amplitude makes a sound soft (like whispering). |
| Example | The screech of a violin string (high pitch) vs. the deep rumble of a bass drum (low pitch). | A whisper (low loudness) vs. a shout (high loudness). |