Math, Science and Sound Activities

By popular demand, I have added this activity page as a follow up to my Math, Science and Sound program. You will find that it focuses on the physics of sound and is organized into two main sections: Waves and Frequency.

My recommendation is to have your students work from top to bottom since the topics flow in a logical sequence. I start by recapping some of the key points from my presentation, then I follow up by including extended activities with sounds, animated graphics, and fun facts. Lastly, if you are a student, you have my permission to use any of my artwork, tables or graphics for a school science fair project. Now, start exploring!

Sound is a form of energy. It travels from one place to another through a medium like air. It can also travel through other gases such as helium, and can even travel through liquids and solids. The only thing sound cannot travel through is a vacuum like space.

When an object moves back and forth, or vibrates, it pushes the air molecules next to it. As air molecules get compressed into waves, the energy is transferred from molecule to molecule until it is exhausted. That is why sounds that are farther away sound softer — their energy fades as they travel.

Question: Is there sound in space?

Hint: Space is an empty vacuum with no air.

Answer: Sound is a form of energy that travels through a medium like air. In space, there is no sound because there is no air. How can astronauts hear each other in the spacecraft? It's simple — the spacecraft is filled with air!

To see and hear how strings vibrate in fractions and produce sound, please see my activity on Standing Waves.

Sounds can be soft or loud. This characteristic of sound is called amplitude or volume. Volume measures the amount of energy in sound waves. More energy will move more air molecules and will sound louder. Less energy will move fewer air molecules and will sound softer. The amount of energy in a sound wave is measured in decibels (dB). To see a decibel chart with some familiar sounds, please see below.

Question: What was the loudest sound ever described by humans?

Hint: It was produced by the most famous volcano in recorded history.

Answer: In 1883, the Krakatoa volcano in Indonesia erupted and threw ash and stone 300 square miles. The explosive sound from this eruption was heard 3,000 miles away. That's the distance from San Francisco to New York City.

Question: What was the loudest animal sound ever measured?

Hint: It was made by the largest animal on the earth.

Answer: Blue whale communication has been measured up to 188 decibels, making it the loudest recorded sound from a living source. These underwater sounds have been detected 530 miles away.

Sound waves travel at different speeds depending on the temperature of the air. At 44 degrees Fahrenheit, sound travels approximately 1,100 feet per second, or 750 miles per hour. To put this into perspective, sound waves travel the distance of 3 1/2 football fields every second, or approximately 1 mile every 5 seconds.

Question: If the air temperature rises, would sound waves travel faster or slower?

Hint: As the temperature rises, molecules bump into each other more quickly, allowing the energy from the sound wave to travel more quickly.

Answer: As the air temperature rises, sound waves travel faster. For example, at 32 degrees Fahrenheit, sound waves travel through the air at 1,087 feet per second, or 742 miles per hour. However, at 100 degrees Fahrenheit, sound waves would travel at 1,163 feet per second, or 794 miles per hour!

Question: Do sound waves travel even faster through liquids and solids?

Hint: Molecules are pushed together more tightly in liquids and solids, allowing the energy of the sound wave to travel more quickly.

Answer: Sound waves travel through liquids and solids much quicker than air. For example, sound waves travel 4 1/2 times faster in water, or approximately 1 mile per second. In a solid like iron, sound waves travel 15 times as fast, or 3 miles per second. Now, can you guess why people used to put their ear to the track to listen for approaching trains?

Knowing that sound waves travel through the air at 1 mile every 5 seconds, you can estimate the distance of a thunderstorm with my Thunderstorm Stopwatch activity.

Sounds can be low like a growling tiger or high like a chirping bird. This characteristic of sound is called pitch or frequency. Objects which vibrate faster produce a higher frequency, and objects which vibrate more slowly produce a lower frequency. The frequency of a sound is equal to how many times it vibrates each second. Vibrations per second are measured in Hertz (Hz).

An object that vibrates 1 time each second would have a frequency of 1 Hertz (Hz).

An object that vibrates 5 times each second would have a frequency of 5 Hertz (Hz).

Question: If you make a musical instrument shorter, will it have a higher or lower frequency?

Hint: A piccolo is 12 1/2 inches long, however, if you stretched out a tuba it would measure 27 feet!

Answer: Shorter instruments produce a higher pitch or frequency. Sound waves can travel, or vibrate, through a shorter tube faster than a longer tube. The faster sound waves vibrate, the higher the vibrating frequency will be. You will see and hear how this works later with the panpipes activity.

If you would like to hear and play frequencies, check out my Tone Synthesizer.

First, let's start with your hearing. Humans can hear between 20 Hz - 20,000 Hz. However, some animals can hear lower or higher than humans. Sounds that are lower than human hearing (below 20 Hz) are called Infrasound. Sounds that are higher than human hearing (above 20,000 Hz) are called Ultrasound. Please see the chart below to compare your hearing to some animals you may have studied.

Zoo Activity on Infrasound: Next time you're at the zoo, observe some of these animals — they could be vocalizing sounds below human hearing. Ask yourself the following questions.
 Is the hippo just yawning or is it vocalizing sounds we cannot hear?       Why does the giraffe seem so quiet?         Why would a herd of elephants suddenly perk up their ears and begin running in one direction?

Animals which use Ultrasound: Listed below are three animals that are predators and three that are prey. Bats eat moths, shrews eat grasshoppers, and cats eat mice. These relationships are based on their ability to interact using sounds above our hearing.
 Why do bats fly with their mouths open? They are vocalizing high frequency chirps that bounce or "echo" back to them. This form of navigation is called echolocation. A bat can fly through a dark cave and catch moths in mid-air using echolocation.     Why do grasshoppers need to hear frequencies up to 50,000 Hz? They are listening for predators like the shrew — the smallest of all land mammals. Shrews are insect-eating animals called insectivores, and they use echolocation to locate crunchy little snacks like the grasshopper.   Have you ever heard the phrase, "quiet as a mouse?" It's not that mice are quiet, it's just that much of their communication is ultrasonic. When a baby mouse calls for its mother, it does so at 40,000 Hz — and adult mice can communicate up to 70,000 Hz! Compare this to the hearing range of a cat and you will understand how high-frequency communication can be a survival strategy.

Question: What animal can hear the lowest frequencies?

Hint: It is a migratory bird.

Answer: Pigeons can hear frequencies as low as .1 Hz, or one vibration every ten seconds! This allows pigeons to hear the infrasonic sounds of ocean waves breaking on the coastline. By positioning their flight path according to coastlines, pigeons can accurately navigate long migrations.

Question: What animal can hear the highest frequencies?

Hint: It is an insect.

Answer: Noctuid Moths can hear up to 240,000 Hz! For a moth, the most important job every night is to avoid being eaten by echolocating bats. After hearing a bat's ultrasonic chirps, a moth will quickly fly away to get out of the bat's detection range.

Hear subtraction! You can determine the difference in frequency by listening to the beat patterns from two sound waves. How does this happen?

If you would like to make a musical instrument that plays different pitches or frequencies, try my Panpipes .  Notice as the pipes get shorter, the pitch or frequency gets higher.  This happens because sound waves can travel, or vibrate, a short distance faster than a long distance.  You see, the pipe is not vibrating, rather it's a column of air inside the pipe that's vibrating.  When the column of air vibrates up and down the pipe at a faster rate, we say it has a higher frequency.  As you will note, my activity includes only musical pitch names (C, D, E, G, A) for each tube.  If you would also like the frequencies for each tube, here they are: C: 523Hz; D: 587Hz; E: 659Hz; G: 784Hz; A: 880Hz.

To make an instrument that involves measuring water, check out my Water bottle Xylophone .  When you add water to a bottle, the pitch or frequency gets lower. This happens because as you add water, you also add more mass to the bottle — the combined mass of the bottle plus the water.  More mass results in a slower/lower vibrating frequency, and less mass produces a faster/higher vibrating frequency.  Again, my activity includes only musical pitch names (F, G, A, C, D) for each bottle.  The corresponding frequencies are: F: 698Hz; G: 784Hz; A: 880Hz; C: 1,046Hz; D: 1,175Hz.

My favorite sounding homemade musical instrument is the Tubular Glockenspiel .  As you will see and hear, the longer you make each metal tube, the lower the pitch or frequency.  Strictly speaking, it's not the length of the metal tubing that determines the frequency, rather it's the mass of the tube.  Since we're using metal tubing with a fairly consistent thickness, all we have to do is increase the length to obtain a corresponding increase in mass.  As with the water bottle xylophone, more mass results in a slower/lower vibrating frequency, and less mass produces a faster/higher vibrating frequency.  Once again, my activity includes only musical pitch names (D, E, F#, A, B)   The corresponding frequencies are: D: 587Hz; E: 659Hz; F#: 740Hz; A: 880Hz; B: 988Hz.

If you are interested in making an instrument that is based Pythagorean fractions, check out my Fraction Tubes .  Just like the panpipes above, as the tubes get shorter, the pitch or frequency gets higher.  The length of each tube is determined by a simple set of fractions derived from the mathematician Pythagoras.  As you will note, my activity includes only musical pitch names (A, B, C#, E, F#) for each tube.  If you would also like the frequencies for each tube, here they are: A: 220Hz; B: 247Hz; C#: 277Hz; E: 329Hz; F#: 370Hz.

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