Frequency, Pitch, and Loudness Differences 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. Repetitive sounds can be formed in different ways. Common, of course, is from a musical instrument.
Understanding Pitch and Frequency
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? Something 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 physicist 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
Consider the Earth going around the sun. Is this motion repetitive? What would an oscillation correspond to? 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.
Loudness and Amplitude
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. Amplitude plays the dominant role in loudness perception. If a sound is played at 50 dB and then the same sound is played at 70 dB, our brains interpret the 70 dB sound as louder.
How far you are from the source of the sound and intervening material also affect loudness. It depends on what is detecting the wave sound, such as an ear.
Tone Quality and Timbre
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.
Frequency's Role in Loudness Perception
However, frequency also plays a role in loudness perception- a 70 dB tone at 1000 Hz and a 70 dB tone at 16,000 Hz will not be perceived as equally loud, even though the intensities are the same. (For most people, the 1000 Hz version will seem much louder). The 1,000 Hz tone will seem far louder than the 50 Hz tone for most people, even though the sound levels are identical. Our ears are especially sensitive to sounds with frequencies between 300 Hz to 3000 Hz. This is fortunate- most human speech takes place in this frequency band.
Equal Loudness Contours and Phons
Hearing tests can be used to construct equal loudness contours. The listener compares tones at different frequencies and is asked to adjust the amplitude of one of the tones until the two tones sound equally loud. For best results, you will need good quality over-the-ear headphones. This frequency plot and ones like it are sometimes called equal loudness contours or Fletcher-Munson curves (after the researchers who did groundbreaking research on the perception of loudness). Frequency is plotted along the x-axis and sound level is plotted on the y-axis. The bottom curve represents all sounds at the threshold of human hearing. Points along this trace are barely perceptible for most people. Barely noticeable sounds at low frequency must have a high sound level to be heard (70 dB for 20 Hz). Similarly, sounds above 10 kHz must be quite intense to be noticed. By contrast, the center of the graph shows that sounds near 1000 Hz don’t have to have be very intense to be heard.
Equal loudness curves are the basis of a unit of loudness called the phon. The phon is an attempt to put a unit on human perception of loudness of pure tones.
Sound Level Meters and Weighting
Equal loudness curves play a role in sound level meters. Since loudness is not measurable, engineers who design sound level meters transform the data picked up by a microphone into a number that reflects the overall loudness of a sound for most listeners. Sound meters use a technique called weighting to compensate for the fact that some frequencies sound louder than others. Weighting uses equal loudness curves to put more emphasis on frequencies humans hear well while downplaying the role of other frequencies play in the overall intensity. A-weighting is the most common scheme, but many experts prefer C-weighting.
| Weighting Type | Description |
|---|---|
| A-weighting | Most common, emphasizes frequencies humans hear well. |
| C-weighting | Preferred by some experts. |