Units
Pressure:
Pascal (Pa) |
= |
1 N/m2 (also equal to 10 dyne/cm2) |
Bar: 1 bar |
= |
105 Pa |
Torr: 1 torr |
= |
133.22 Pa |
Sound wave pressures fall in the range between 0.00002 Pa or 20 μPa), corresponding approximately to the average ear’s threshold at around 3–4 kHz, to about 200 Pa, generally reckoned to be about the pain level.
Intensity
Watts/m2 (W/m2), or, more practical in sound, μW/m2.
Velocity of Sound, Typical Values
See table opposite.
A general expression for the velocity of sound in gases is given by:
c = (γP/ρ)−2
where γ is the ratio of the specific heats of the gas (1.414 for air), P is the pressure and ρ is the density of the gas.
Frequency (f) and wavelength (λ)
These are related by the expression
c = fλ
Note that this formula applies to all waves. In the case of electromagnetic waves (radio, light etc.) c is approximately 300 000 km/s (3 × 108 m/s) as opposed to about 340 m/s for sound waves in air. The formula could be used only with caution for surface waves on water as the velocity of the waves can vary with amplitude.
Velocity of sound, typical values
Substance |
c (m/s) |
Air, 0°C* |
331.3 |
Hydrogen, 0°C |
1284 |
Oxygen, 0°C |
316 |
Carbon monoxide, 0°C |
337 |
Carbon dioxide, 18°C |
266 |
Water, 25°C |
1498 |
Sea water, 20°C |
1540 |
Glass |
~5000 |
Aluminium |
5100 |
Brass |
3500 |
Copper |
3800 |
Iron (wrought) |
5000 |
Iron (cast) |
4300 |
Concrete |
3400 |
Steel |
5000–6000 |
Wood, deal, along grain |
5000 |
oak |
4000–4400 |
pine |
3300 |
* The velocity of sound in air increases with temperature by approximately 2/3 of a m/s per °C rise in temperature. More accurately: c = 331 + 0.6t where t is the temperature in °C.
Sound wavelengths in air at 20 °C
Frequency (Hz) |
Wavelength (m) |
16 |
21.43 |
20 |
17.15 |
30 |
11.43 |
50 |
6.86 |
100 |
3.43 |
200 |
1.72 |
500 |
0.69 |
1 000 |
0.34 |
5 000 |
0.069 |
10 000 |
0.034 |
16 000 |
0.021 |
Intensity (I) falls off with distance (d) according to:
Pressure, on the other hand, follows the law:
The Doppler Effect
Assuming a stationary medium, if the source is moving towards the observer with velocity vs then the apparent frequency, fa, is given by
If the observer is moving towards the source with velocity vo then
The Musical Scale
The table opposite shows the equal-tempered scale, where the ratio of the frequency of one note to the next one above it is 
or 1.059 463 1.
Frequencies of Vibrations in Pipes and Strings
Pipe open at one end:
where n = 1,2,3 etc. l is the length of the pipe and a is the end correction.
For a pipe with a significant flange a is roughly 0.8r, where r is the radius.
Note |
Frequency (Hz) |
A |
220.00 |
A# |
233.08 |
B |
246.94 |
C |
261.63 |
C# |
277.18 |
D |
293.66 |
E |
311.13 |
E# |
329.63 |
F |
349.23 |
F# |
369.99 |
G |
392.00 |
G# |
415.30 |
A |
440.00 |
A# |
466.16 |
B |
493.88 |
C’ |
523.25 |
Figure 3 Portion of a keyboard
Figure 5 Standing wave patterns
(Frequencies of vibrations in pipes and strings, continued from page 14)
In the case of an unflanged pipe a is about 0.6r.
Pipe open at both ends:
The velocity of a transverse wave in a string of tension T and mass m per unit length:
The lowest frequency of vibration in such a string is then
Some Italian terms found in music