Wave Speeds

The propagation speeds of traveling waves are characteristic of the media in which they travel and are generally not dependent upon the other wave characteristics such as frequency, period, and amplitude. The speed of sound in air and other gases, liquids, and solids is predictable from their density and elastic properties of the media (bulk modulus). In a volume medium the wave speed takes the general form

This relationship works fairly well for water with tabulated values:

This agrees well with the measured speed of sound in water, 1482 m/s at 20°C. The situation with solids is considerably more complicated, with different wave speeds in different directions, in different kinds of geometries, and differences between transverse and longitudinal waves.

For example, a general tabulated value for the bulk modulus of steel gives a sound speed for structural steel of

Comparing to one tabulated example for stainless steel shows wide variation between the speed for longitudinal and transverse waves, with this calculated value somewhere in between.

Sound Speed in Liquids

Selected Sound Speeds in Metals

• V_l = velocity of plane longitudinal wave in bulk material
  V_l 是在 bulk 材料中平面纵波的速度
• V_s = velocity of plane transverse (shear) wave
  V_s 是横波（剪切波）的速度
• V_ext = velocity of longitudinal wave (extensional wave) in thin rod
  V_ext 是薄杆中纵波（伸张波）的速度

Temperature from Sound Speed

The speed of sound in liquids depends upon the temperature. This is useful in monitoring the temperature of oceans and other large bodies of water because pulses of low frequency sound can travel thousands of kilometers through the ocean and still be detected. The pulse traverse time can be measured with a network of stations to monitor changes in the temperature of the intervening water. When compared to changes predicted by climate models, this can give some indication of whether global warming from the greenhouse effect is occurring.

Ocean experiments are capable of showing temperature variations in the range of hundredths of degrees. Experiments under the north polar icecap indicated a half degree of warming in 10 years. Larger scale experiments between California and Hawaii have been delayed for an assessment of possible damage to marine life.