F.E.Newing and Richard Bowood, The Ladybird Book of The Weather (Loughborough: Wills & Hepworth Ltd., 1962), 18-19. Illustration by Robert Ayton.
“Over open ground, substantial vertical wind velocity gradients commonly exist due to friction between the moving air and the ground. Wind speed profiles are strongly dependent on the time of day, weather conditions and the nature of the surface. The wind speed, in the absence of turbulence, typically varies logarithmically up to a height of 30 to 100 meters, then negligibly thereafter. As a result of this velocity gradient (and the resulting change in sound velocity which it causes), a sound wave propagating in the direction of the wind will be bent downward. In the upwind direction the sound speed decreases with altitude, sound waves are directed upward, away from the ground, forming a “shadow zone” into which no direct sound penetrates (Figure 3). This process is called refraction, whereby the path of sound waves curves in the direction of the lower sound velocity. The radius of curvature of the sound path is inversely proportional to the velocity gradient. Sound always refracts toward the lower sound speed.”1
1. John S. Lamancusa, Noise Control (Pennsylvania: Pennsylvania State University, 2000), np.
On a freakishly dry, still January day in upland Montgomeryshire a test is conducted. A lone figure stands a short distance north of the triangulation point on Garreg-hir (SN 9985 9788) and loudly but clearly annunciates the words ‘sound propagation’. At the same moment an equally lone figure (of identical stature to the annunciator and with unparalleled hearing) stands on the ridge line to the north-west of Blaen-y-Cwm (SN 9836 9884).
The annunciator stands at 484 metres above sea level whilst the receiver with unparalleled hearing stands 450 metres above sea level—taking into account difference in altitude the distance between the two lone figures is 1782.28 metres. Down in the valley below at Caersws the temperature has crept above zero as the day has progressed and is currently 4.6oC. Caersws is at an altitude of 124 metres above sea level and is thus warmer than Garreg-hir by some 2.304oC and warmer than the receiver’s position by 2.0864oC (assuming a temperature decrease of 6.4oC per 1000 metres of altitude).
For the purposes of the test the temperature at the locations of the annunciator and the receiver will be averaged to 2.1952oC. Assuming that the speed of sound is 331.4 + 0.6cT m/s then at the upland temperature of 2.1952oC the speed of sound is 332.7390 m/s. From the instant that the annunciator commences his proclamation the words will take 5.3563904 seconds before they begin to unfold in the unparalleled auditory equipment of the receiver.
Furthermore, the words ‘sound propagation’ are fully annunciated in 1.67 seconds so this complete transmission will take 7.0263904 seconds. Whilst the test is conducted the words ‘sound propagation’ will occupy 555.67413 metres of linear/horizontal space of unknown breadth and height.