Speed of Sound

1. Speed of Sound

2. The Speed of Sound (sec 7.3) • The speed of any wave depends upon the properties of the medium which the wave is travelling. • Two essential properties which effect wave speed • Inertial Property – the density of the material • The greater the inertia of the particles in the medium the less responsive they will be to interactions with neighbouring particles • If other factors are equal, a wave will travel faster in a less dense material (just like light) • Sound will travel faster in Helium than in air; helium particles have less mass than air particles

3. The Speed of Sound • Elastic Properties – related to the tendency of a material to maintain its shape or not deform whenever a force or stress is applied to it • Steel is a rigid material with high elasticity. It’s particles have strong interactions to prevent deformation and maintain its shape if a force or stress is applied • Rubber band – it deforms or changes shape readily. • The phase of matter has a significant impact upon elastic properties of medium • In general solids have the strongest interactions between particles compared to liquids and gases. • For this reason, longitudinal sound waves travel faster in solids than in liquids or gases.

4. The Speed of Sound • The transmission of sound waves is really a series of chain reactions of collisions between adjacent molecules. In general, the closer these molecules are together, the faster the sound travels. • Therefore, for sound waves vsolid > vliquid > vgas

5. The Speed of Sound • The speed of sound is also affected by temperature – why? • Temperature will effect the strength of the particle interactions (elastic property)

6. Speed of Sound in Air • The speed of sound in air is 332 m/s at 0oC. The speed increases by 0.59 m/s for each increase of 1oC. Equations: Where: vs = speed of sound in m/s Temp = the air temperature in oC Variation:

7. Your Turn!! • What is the speed of sound in air when the temperature is 25oC? • Try question #3 on pg 243 in textbook. • More practice • pg 243 #2, 4 • pg 246 #1,2,3,5,6,7,8

8. Doppler Effect (sec 7.10) • What do you notice about the frequency (pitch) of the sound of an ambulance as it: • Approaches you? • The frequency gets higher • Moves away from you? • The frequency gets lower • Why? • Video Clip#1 • Video Clip#2 • See figure 1 on page 268 in your text

9. Doppler Effect • Occurs when the source of a sound is moving away or towards the observer • As the sound waves approach the observer, they are closer together than they would be if the source was stationary • Shorter wavelength = higher frequency = higher pitch • As the sound waves travel away from observer, they are farther apart • Longer wavelength = lower frequency = lower pitch

10. Doppler Effect

11. Doppler Effect • The effect of speed on the frequency is given by the following formula • Where vs = speed of sound in medium vo = speed of source through medium fo = original frequency of sound from source f = frequency of sound heard by stationary observer • Note: use vs + vo if source moving away from observer use vs – vo if source moving towards observer

12. Your Turn!! • Try Q#2 on page 272 in textbook • Given: fO = 520 Hz vo = 26 m/s vs = 344 m/s • Required: f = ? Hz (frequency heard by observer) • Equation: since source is moving away from observer • Substitute: • Solve: • More Practice: pg 269 #1,2 and pg 272 #1

13. Mach Number • Subsonic speed – speeds less than the speed of sound in air • Supersonic speed – speeds greater than the speed of sound in air • Mach number of a source of sound is the ratio of the speed of sound of the source to the speed of sound in the air • Practice: pg 270 #3,4,5 and pg 272 #3,4 and Problem Set