1. Why Flutes Sound Higher on Hot Days: Sound Speed and Air Resonance
In wind instruments like flutes, sound is produced by the resonance of air inside the tube. Once the length of the tube is fixed, the length of the resonating wave is also fixed. If the wave length stays the same, an increase in the speed of sound leads to an increase in the number of waves vibrating per second (frequency), making the pitch higher [1]. Imagine rolling a ball from one end of a classroom to the other. The faster the ball, the more trips it can make in one second. Sound in a tube works similarly: the faster it goes, the more cycles occur. However, in reality, sound is not a single block moving back and forth, but overlapping waves.
The speed of sound is determined by air temperature. At 0°C, it is about 331 meters per second. At 20°C, it is about 343 meters per second [2]. The difference is 12 meters, which calculates to about 3.6%, not even reaching 4%. For every 1°C increase, the speed increases by approximately 0.6 meters per second.
2. Why Air Molecules Move Faster Than Sound
Air molecules are not still. They fly around in all directions at tremendous speeds. The higher the temperature, the more vigorous their movement. At 20°C, nitrogen molecules, which make up a large part of air, move at an average speed of about 510 meters per second [5]. This is faster than the speed of sound (343 meters). Yet, sound is slower than the molecules because the molecules are not carrying the sound themselves. Molecules collide with other molecules, so they cannot travel very far in one second [5]. What is transmitted is only the message that "this place was pushed" [2]. This is why a smell takes much longer to reach the other side of a room than sound does; molecules have difficulty moving forward.
Imagine a square filled with people, all moving around. If you pass a signal by tapping the person next to you on the shoulder, the signal passes faster if everyone is moving busily, because you bump into the next person sooner. Warm air is like a square where everyone is moving energetically. However, in reality, molecules are not trying to pass on a signal; force is simply transmitted through collisions.
3. Why Sound Speed Is Not Proportional to Temperature: Mountains, Humidity, and Newton’s Calculation
The speed of sound is not proportional to temperature. Therefore, the speed of sound does not become zero at 0°C; it still travels at about 331 meters per second. What else affects it besides air temperature? It is explained that air pressure (atmospheric pressure) does not change the speed of sound if the temperature is the same. If sound were slower on a high mountain, it would not be because the air is thin, but because it is cold [3]. The effect of water vapor (humidity) is small, increasing the speed by only about 0.1 to 0.6% [3].
Newton also calculated this speed of sound. In his 1687 work "Principia," it is said he calculated the speed of sound in air as 979 feet per second (about 298 meters in modern units), which was more than 10% lower than the actual value. The cause is explained as treating the compression and expansion of air as isothermal (temperature constant) when sound passes through. Later, Laplace is said to have corrected this by considering temperature changes [3]. About 50 years later, in 1738, the Paris Academy of Sciences obtained a value of 332 meters per second at 0°C with no wind, using a cannon experiment. The difference from the current value was within 1% [3].
4. How Fast Sound Travels in Water and Iron Compared with Air
In fresh water at 20°C, sound travels at about 1,480 meters per second. This is about 4.3 times faster than in air [2]. In iron, values range from 5,000 to 6,000 meters per second depending on the source, which is about 15 to 17 times faster than in air [2][3][4]. Let us compare the time it takes for sound to reach 100 meters away. In air, it takes about 0.3 seconds. In iron, it takes about 0.02 seconds.
Water and iron are much heavier (higher density) than air, yet sound is faster. This is because the speed of sound increases with stiffness and decreases with density [3]. Water and iron are difficult to compress and have an overwhelming pushing-back force. This effect outweighs the effect of weight. It is said that in water, sound also becomes faster as the temperature rises [3]. However, this article does not address whether this can be explained by molecular movement like in air.
5. Why Sound Bends and Is Heard Differently in the Day and at Night
If the air temperature differs from place to place, the speed of sound also differs from place to place. As a result, the direction of sound travel bends. This is sound refraction. The sound bends toward the side where the speed is slower. For example, if one side of a car’s tires enters mud, the car turns toward the mud. It is similar. However, in reality, sound is not a single object but a spreading wave.
During the day, the ground is warm and the upper air is cold. Since sound becomes slower as it goes higher, sound bends upward and becomes harder to reach the ground. At night, the area near the ground cools, and sound bends downward, sometimes reaching far away. It is explained that the same thing happens in winter [6]. The formation of a "sound shadow," where sound bends due to temperature changes with height and becomes hard to hear, is also written in other materials [3]. Since nights are quieter and easier to hear, it cannot be said that bending alone explains everything.
6. Measuring Temperature with Sound Speed: Ultrasonic Thermometers and Sound on Mars
If the speed of sound is determined by temperature, then conversely, measuring the speed of sound reveals the temperature. Using this idea, there is an "ultrasonic anemometer and thermometer" that measures wind speed and temperature simultaneously. In 1966, Mr. Yoru Mitsuda of the Disaster Prevention Research Institute at Kyoto University published the "General-purpose Ultrasonic Anemometer and Thermometer" in the Journal of the Meteorological Society of Japan [7].
The speed of sound was also measured on Mars. It was reported in "Nature" on April 1, 2022, based on sounds recorded by the microphone of NASA’s Perseverance rover [8]. On Mars, low sounds traveled at about 240 meters per second, and high sounds at about 250 meters per second. Compared to Earth’s about 343 meters, this is about 70% [8]. The air on Mars is cold, thin, and made of carbon dioxide. This affects the speed of sound. The fact that the speed differs by pitch is reported as a characteristic of Mars’s low-pressure carbon dioxide atmosphere, not a story about Earth’s air [8].
7. How to Investigate Sound Speed Yourself: Calculating Arrival Time at 0°C and 20°C
Let us calculate. How much difference is there in the time it takes for sound from 100 meters away to arrive at 0°C versus 20°C? At 0°C, 100 ÷ 331 is about 0.30 seconds. At 20°C, 100 ÷ 343 is about 0.29 seconds. The difference is only about 0.01 seconds. Still, can you explain why the pitch of a flute changes using the ball analogy from Section 1?
The story of sound on Mars begins with the NASA article [8]. If the speed differs for low and high sounds, how does the way distant sounds are heard change? Is "distant sounds are audible at night" because sound bends, or because it becomes quiet? How much each factor contributes is not clear in this article. Think of a scene where you noticed this and consider both possibilities.