WAVES AND SOUND SPH3U WAVE THEORY • Robert Hooke in 1665 proposed the idea of a wave theory used to predict how waves behave. • 20 years later, Christiaan Huygens (1629-1695) postulated: "Every point on a wave-front can be considered as a point source of tiny secondary wavelets that spread out in front of the wave at the same speed as the wave itself. The surface envelope, tangent to all the wavelets, constitutes the new wavefront." • This was a useful theory to predict the future position of waves. WAVE THEORY • The straight line travel of waves is called rectilinear propagation. • This is clearly evident with light where sharp shadows are produced and we can not see around corners! • The source producing a wave supplies energy which is transmitted in the form of a disturbance. (Sound, explosions, tidal waves) TERMINOLOGY • Wavelength: (λ) The distance between adjacent crests or troughs of a wave. (Measured in metres) λ • Period: (T) The time it takes for a wave to travel one wavelength. The time for one complete cycle. Measured in seconds. • Frequency: (ƒ) The number of waves passing a fixed point every second or the number of cycles per second. The inverse of period, measured in Hertz. (Hz, s-1) The frequency of a wave remains constant as it is determined by the source. • Ƒ = 1/T UNIVERSAL WAVE EQUATION • A wave travels a distance equal to its wavelength in a time equal to its period. d v t is modified as and is finalized as v = ƒλ  v T WAVE TYPES • Transverse Waves: A wave in which the wave’s components move perpendicular to the direction of motion of the wave. Wave direction of travel Examples: Water waves, All EM waves (Light, etc) and waves in springs. WAVE TYPES • Longitudinal waves: A wave in which the wave’s components move parallel to the direction of motion of the wave. The wave consists of compressions and rarefactions. Examples: Sound waves, waves in springs SOUND • Sound is a longitudinal wave composed of compressions and rarefactions. • Compressions occur where the molecules are close together. • The pressure of the air molecules oscillate around an average value. (Mean air pressure) • The air molecules are in constant random motion and collide to transmit energy away from a sound source. SOUND • Sound moves at 332 m/s at 0oC and 1 atm. • As temperature increases, so does molecular motion and therefore the speed of sound. • Sound waves are transmitted through some medium to a listener (there is no sound in space). 332𝑚 0.6 𝑚/𝑠 𝑣= + [𝑇] 𝑠 𝑜𝐶 EXAMPLES • Find the speed of sound at 16.0oC. 332𝑚 0.6 𝑚/𝑠 𝑣= + [𝑇] 𝑠 𝑜𝐶 v = 332 m/s + (0.6 m/s/oC)(16.0 oC) = 342 m/s EXAMPLES • Thunder is heard 8.0 s after lightning is seen. If T = 30.0oC, how far away was the lightning? • Assume the observation of the light was instantaneous (as light is much faster than sound). 332𝑚 0.6 𝑚/𝑠 𝑣= + [𝑇] 𝑠 𝑜𝐶 v = 332 m/s + (0.6 m/s/oC)(30.0 oC) = 350 m/s d = vt d = 350 m/s(8.0 s) = 2.8 km EXAMPLES 332𝑚 0.6 𝑚/𝑠 𝑣= + [𝑇] 𝑠 𝑜𝐶 • A biologist is dropped into an 80.0 m deep dry well for safekeeping. How long after dropping him will you hear the sound (if T = 20.0oC) of his body hitting the ground at the bottom? • Part 1: Find time to free fall to bottom (Kinematics formulae) • Part 2: Find time for sound to travel back up to our ears. (d = vt) • 4.04 s + 0.23 s = 4.27 s CHALLENGE QUESTION • You drop a rock into a well and 5.37 s later you hear the splash. If T = 16.0oC, how deep is the well? CLASS/HOME WORK • Sound worksheet • Textbook work on sound speed, etc.