as 965 (at 0°C) there is relative movement between the source and the observer. Air (dry) 331 (at 0°C) (The Doppler Effect applies to all waves, but here we are concerned only with sound.) For a source moving with velocity V towards the observer the apparent sound frequency is given by Equation 8.6. Ageneral expression for the velocity of sound in gases is given by Equation 8.3, where Y is the ratio of the specific heats of the gas (8.6) (1.414 in the case of air), P is the pressure and p is the density of the (8.3) Taking c as 340m/s and a source velocity of 10m/s, then a sound of true frequency 1kHz would be received as 1030.3Hz (from Equation 8.6) For an observer moving with velocity V towards a stationary It follows that, provided the gas obeys Boyle's Law, increasing the source, apparent sound frequency is given by Equation 8.7. pressure will increase the density in the same proportion, SO that under constant temperature conditions the velocity C is independent of pressure. Increase of temperature, however, causes expansion SO f = Mctvol (8.7) that, under constant pressure conditions, an increase in temperature results in a decrease in density. To summarise, an expression show- ing how C (in m/s) varies with temperature, t (in °C), is given by Again taking C as 340m/s and the observer's velocity as 10m/s, a Equation 8.4. sound of frequency 1kHz would be received as 1029.4Hz (from Equation 8.7). c = 331 + 0.61 (8.4) Note that for the same relative velocities the apparent change in frequency depends on whether it is the source or the observer which Therefore at -10°C the value of c is 325m/s; at 0°C it is 331m/s; is in motion. When the relative velocity approaches c the apparent at 10°C it is 337m/s; at 20°C it is 343m/s. A fair approximation at frequency for a moving source approaches infinity, whereas for a normal temperatures is 340m/s. moving observer the frequency approaches 2f. 8.1.3 Frequency and wavelength 8.2 Decibels The frequency of any wave is defined as the number of complete waves emitted or rece