Gases – Speed of Sound

Understanding the Speed of Sound in Gases

The speed of sound tells you how quickly tiny pressure disturbances travel through a gas. For an ideal gas, the governing relation is \( c = \sqrt{\gamma\,R\,T} \), where \( \gamma = c_p/c_v \) (heat-capacity ratio), \( R \) is the specific gas constant, and \( T \) is absolute temperature in kelvins. This compact formula explains most of the trends you’ll see in the table: sound is faster in lighter gases, in gases with smaller heat capacity (larger \( \gamma \)), and at higher temperatures.

Why helium and hydrogen are “fast,” and SF₆ is “slow”

The specific gas constant is \( R = \bar{R}/M \), where \( \bar{R} \) is the universal gas constant and \( M \) is molar mass. Light molecules (helium, hydrogen, neon) have large \( R \), pushing \( c \) upward. Heavy, polyatomic molecules (sulfur hexafluoride, carbon tetrachloride) have smaller \( R \) and usually smaller \( \gamma \) because they store energy in rotational and vibrational modes—both effects reduce sound speed. Monatomic noble gases (He, Ne, Ar, Kr) are simpler: their \( \gamma \approx 5/3 \) is comparatively high, so even at the same temperature, they carry sound faster than many multi-atom gases.

Temperature matters via a square-root law

If composition is fixed, temperature is the dominant variable. Because \( c \propto \sqrt{T} \), going from 0 °C (273.15 K) to 20 °C (293.15 K) increases \( c \) by about \( \sqrt{293.15/273.15} \approx 1.036 \) — roughly a 3.6% bump. That’s why this tool lets you “normalize” a published speed from its base temperature \( T_0 \) to your chosen target \( T_1 \):

\( c(T_1) \approx c(T_0)\,\sqrt{\dfrac{T_1+273.15}{T_0+273.15}} \)

Tip: Normalization is most reliable near room temperature and ordinary pressures, where ideal-gas behavior is a good approximation.

Does pressure change the speed of sound?

At first glance, you might expect denser air to transmit sound faster. For ideal gases, not quite: if the gas composition and temperature are unchanged, pressure cancels out of the formula. That’s why sea-level and high-altitude air at the same temperature have nearly the same \( c \). Pressure only matters indirectly—by influencing phase (e.g., steam at 6 MPa) or composition (e.g., moisture content limits).

Humidity and mixtures

Real air is a mixture. Adding water vapor changes the effective \( R \) and \( \gamma \), nudging \( c \) upward by about 0.5–1% when going from bone-dry to ~50% relative humidity at 20 °C. In specialty gases, trace components can matter too (e.g., CO₂ in “air” for lab work). Our companion tool Air — Speed vs Temperature models this moist-air effect explicitly.

When the simple model breaks down

• Very high pressures / near condensation: Non-ideal effects and changing \( \gamma \) make the square-root scaling less accurate. The “Steam, 6 MPa” row in the table is therefore not normalized.
• High temperatures: Vibrational modes become active; \( \gamma \) declines, so \( c \) grows more slowly than \( \sqrt{T} \) would suggest.
• Reactive or dissociating gases: Composition can shift with temperature, altering both \( R \) and \( \gamma \).

Quick rules of thumb

• Temperature scaling: +10 °C ≈ +1.8–2.0% in many gases near room temperature.
• Molar mass trend: Lower molar mass → higher \( R \) → higher \( c \), all else equal.
• Polyatomic penalty: More internal degrees of freedom → smaller \( \gamma \) → slower \( c \).

From speed to wavelength and Mach

Once you know \( c \), wavelength is \( \lambda = c/f \) (e.g., a 1 kHz tone in air at 20 °C has \( \lambda \approx 0.343 \) m). In aerodynamics and flow acoustics, Mach number is \( \mathrm{Ma} = V/c \). Because \( c \) depends on temperature and gas type, the same vehicle speed may correspond to different Mach numbers in different gases or on different days.

For metrology-grade work across wide ranges, consult full thermophysical property databases that provide temperature-dependent \( c_p \), \( c_v \), and mixture models. For education, quick design checks, and day-to-day acoustics, the ideal-gas picture and the normalization tool here are excellent starting points.