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Colors of noise – You may have heard of white noise; there are many different “colors” of noise pertaining to the frequencies of sound contained within the noise. This wikipedia page allows you to listen to the different types of noise.

Intensities of Various Sounds

DescriptionIntensity (dB)Intensity (W/m2)
Threshold of human hearing010-12
Rustling leaves1010-11
“Normal” conversation40 – 6010-8 – 10-6
Vacuum cleaner7010-5
Heavy traffic9010-3
Loud rock concert120100
Jet airplane150103
Rocket engine180106

Video Transcript

Hello there! Welcome to lecture 21: musical sounds!

What is it that distinguishes music from noise? Why is it that two musical instruments playing the same note sound different from each other? How can we characterize the loudness of different sound waves? All of these questions, and more, will be answered in this lecture video!

Each of the following concepts will be discussed in this video: music versus noise, and loudness versus intensity.

Music versus noise

There’s a practically infinite number of combinations of different frequencies and amplitudes of sound. Some of these combinations may sound pleasing to us, and others may not. Usually, we categorize the pleasing sounds as musical sounds. Perhaps you consider jazz, classical, rock, or rap to be musical. Other sounds that are not pleasing can be categorized as noise. This might include sounds such as banging together pots and pans, or dropping a hammer on the floor. 

What is it that distinguishes music from noise? To a certain extent, this is a subjective question that depends on the person listening to the sounds. You may consider certain types of sounds to be musical, whereas I might consider them to be more like noise. 

From a physics perspective, we can broadly categorize different types of sounds as either music or noise based on the types of frequencies contained in the sound. Most sounds are not pure tones consisting of only a single frequency of sound waves. Instead, they are the combination of a few, or sometimes many, tones combined together.

Using a concept called Fourier analysis, we can look at the different frequencies that make up each sound. The math behind Fourier analysis is very complicated and is outside the scope of this class. However, using software such as Logger Pro, we can record a sound wave and then see a graph of amplitude versus frequency. That is, how many frequencies are represented in a sound wave, and how loud is each of those frequency components?

Let’s consider the Fourier analysis of a few different types of sounds and see how they look!

First, let’s look at the Fourier analysis of the sound made by a tuning fork. [pause] The tuning fork is built to produce a single frequency of sound, although other harmonics can be created in the tuning fork, just as a string can support multiple standing wave harmonics. The Fourier analysis shows a single predominant peak at 490 Hz, the same the frequency stamped on the side of the tuning fork. A few other harmonics exist, at greatly reduced amplitudes.

Next, let’s look at the Fourier analysis of the sound made by a piano. [pause] This piano is playing a single note, but does not produce one single frequency of sound wave. There are more frequencies of waves represented in this sound compared to the tuning fork. Note that the frequencies that do exist are periodic. That is, they are spaced out at regular intervals.

Next, let’s look at a noisy sound, a snap. [pause] This sound creates many frequencies of sound waves, making a rather random-looking Fourier analysis graph. There is no clear pattern to the frequencies in this sound.

Finally, let’s look at the Fourier analysis of a white noise machine. This machine creates many frequencies of sound, creating a very broad spectrum of frequencies that are represented in this sound wave.

What conclusions can we make from this data? Generally speaking, musical sounds, such as the tuning fork and piano, consist of just a few frequencies of sound waves. We call this type of Fourier analysis discrete. Discrete just means that there are only a few frequencies that exist. Sounds that we consider to be noise have very continuous, broad, or random frequency distributions in their Fourier analysis.

One last comment about musical sounds. Musical instruments are designed to support different standing waves and create sounds at different frequencies. For example, the note “middle C” has a frequency of about 260 Hz. If there are five different instruments all playing middle C at the same frequency, what is it that causes each instrument to sound different?

In fact, each instrument will have a slightly different Fourier analysis. The exact frequencies that make up any particular musical note will be a little different from any other instrument. This characteristic is called timbre. It has to do with the design of the instrument, the materials it is made from, and how many harmonics are created in the instrument. 

Loudness versus intensity

Loudness has to do with a subjective quality of the amplitude of a sound wave. Perhaps you like to turn the volume all the way up, and consider that to be the best level of volume for listening to music. Somebody else may consider that same volume to be too loud. For a single individual, loudness is related to the intensity of a sound wave, but among individuals, loudness is not something that can be agreed upon.

On the other hand, intensity describes the amount of energy per unit of area that reaches a certain location every second. In other words, it is equal to the amount of power divided by the area over which that power is distributed. Intensity is an objective, physical quantity, that we could measure. The units of intensity are watts per meter squared. It is related to the energy that is transmitted by the sound wave.

The human ear is capable of hearing sounds that are both very quiet and very loud. This means that the values of intensity that we can hear go from extremely small numbers to extremely huge numbers. The lowest intensity sound that a human ear can hear is 10 to the negative 12 watts per meter squared. That is, a decimal point, eleven zeros, and a one watts per meter squared. On the other end of our ability to hear, a rocket engine has an intensity of 10 to the 6 watts per meter squared. That’s a one with six zeros after it. That’s a huge range of intensity values!

For this reason, using intensity values is not the best way to describe sound intensity. Instead, scientists use a relative scale. In other words, how much more intense is one sound compared to another? To determine the relative intensity of sounds, we divide by some baseline. The baseline that everything is measured relative to is the threshold of human hearing, 10 to the negative 12 watts per meter squared. Now we can see how much more intense one sound is compared to that threshold. The threshold of human hearing has a relative intensity of one. The rocket engine has a relative intensity of 10 to the 18. We’ve gotten rid of very tiny numbers using a relative scale, but we still have an enormous range of values from quiet to loud.

To solve this issue, we use a logarithmic scale to discuss intensity. The logarithm just looks at the exponent of the power of ten, and ignores the base, that number ten that we’re taking a power of. Now our scale of values goes from 0: threshold of human hearing, to 18: rocket engine. We solved the problem of having too many numbers to now having too few numbers to represent different values. 

The decibel scale solves this problem. After taking the logarithm of each relative intensity, we multiply by 10. If you have heard of the decibel scale, this is exactly what we’re measuring. The logarithm of the relative intensity of one sound compared to the threshold of human hearing, multiplied by 10. Many common sounds can be represented with a decibel value, indicating this physical quantity.

At a certain level of intensity, around 85 decibels, our ears will become damaged. People working around loud noises for long periods of time need to wear earplugs or headphones to protect their hearing. If we’re going to be exposed to relatively low intensity noises for short periods of time, earplugs may be sufficient. For longer exposures, or for more intense noises, such as working around jet engines, earmuffs may be needed.

At intense enough levels, sound waves can cause physical pain. That’s around approximately 120 decibels. Above this level, it is important to wear protective equipment on our ears!

Earplugs are used to decrease the intensity of sound. Usually on the label of a package of earplugs is a decibel value that is included. This indicates how much the decibel level will decrease. If I’m using a gas powered leaf blower with an intensity of 90 decibels, wearing 30 decibel earplugs will reduce the intensity to 60 decibels. 

How much more intense (louder, if you will) is a rocket engine compared to a jet engine? This question of “how much louder” becomes slightly difficult to answer when we are using a logarithmic scale. Recall that the logarithm tells us the exponent on the number ten. In other words, it tells us how many zeros are after the one in a number. A jet engine is 150 decibels. Something at 160 decibels is 10 times louder. Something at 170 decibels is 100 times louder. The rocket engine, at 180 decibels, is one thousand times more intense!

So when calculating “how much louder,” remember that every time we increase the decibel value by 10, we are multiplying the intensity by 10. A difference of 10 decibels is 10 times louder, but a difference of 20 decibels is 100 times louder, a difference of 30 decibels is 1000 times louder, and so on.

Thanks for taking the time to learn about musical sounds! Until next time, stay well.