Velocità del suono nei mezzi en
From "Physics, Waves, Music": a website about the physics of waves and sound, acoustics of musical instruments, musical scales, harmony and music.
| AI-translated from Italian. Original page: Velocità_del_suono_nei_mezzi |
Speed of sound
| medium | wave speed | ||
|---|---|---|---|
| longitudinal | transverse | surface | |
| ideal gas |
|
imposs. | imposs. |
| liquid | imposs. | (deep water) | |
| (shallow water) | |||
| solid |
|
||
| bar | |||
| string | |||
Meaning of the symbols
| symbol | meaning | SI unit |
|---|---|---|
| γ | ratio of specific heats | dimensionless |
| K | bulk modulus | Pa |
| shear modulus | Pa | |
| M | molar mass | kg mol-1 |
| p0 | atmospheric pressure | Pa |
| ρ0, ρ | equilibrium density (for the string: linear density) | kg m-3 (string: kg m-1) |
| g | acceleration due to gravity | m s-2 |
| h | water depth | m |
| λ | wavelength | m |
| R | gas constant | J mol-1 K-1 |
| T | absolute temperature (in the gas); tension (in the string) | K; N |
| Y | Young's modulus (elasticity) | Pa |
Typical values
| medium | m s-1 |
|---|---|
| Air at 20 °C | 343 |
| Aluminium | 6300 |
| Brass | 4700 |
| Copper | 4700 |
| Steel | 6100 |
| Water at 20 °C | 1481 |
| Sea water at 13 °C | 1500 |
| Oak wood | 4000 |
See the pages speed of mechanical waves and speed of sound.
Check your understanding
Problem. Calculate the speed of sound in air (γ = 1.4, M = 0.029 kg/mol) at 20 °C and at 0 °C (R = 8.314 J mol−1 K−1).
Solution. At 20 °C (293 K): √(1.4 · 8.314 · 293/0.029) m/s ≈ 343 m/s. At 0 °C (273 K): about 331 m/s. The speed grows as the square root of the absolute temperature, by about 0.6 m/s per degree: this is why wind instruments go sharp as they warm up.Problem. Calculate the speed of sound in helium (γ = 5/3, M = 0.004 kg/mol) at 20 °C. Why does someone who speaks after inhaling helium have a "Donald Duck" voice?
Solution. √(1.667 · 8.314 · 293/0.004) m/s ≈ 1010 m/s, almost three times the speed in air. The resonances of the vocal tract (the formants) are proportional to the speed of sound and shift upwards, while the vibration frequency of the vocal folds changes little: the timbre becomes brighter.Problem. The end of a 1 km long steel rail is struck with a hammer. Someone listening at the other end hears two knocks: how much time passes between them?
Solution. In steel the sound takes 1000/6100 s ≈ 0.16 s, in air 1000/343 s ≈ 2.92 s. The first knock arrives through the rail and the second, about 2.75 s later, through the air.Categories:
