Lecture 16 — Mechanical waves Outline 1 Definition

Lecture 16 - Mechanical waves Outline: 1. Definition and examples of mechanical waves 2. Modeling Mechanical Waves 3. Transverse Waves in String 4. Sound Waves in Air 5. Considerations of Energy, Power, and Area in measuring energy Intensity of Sound and “Loudness” (Level of Intensity) 6. Relating Energy, Intensity and Amplitude of sound 1

Announcements Project report submission • Group leaders must submit the following between 9. 00 am – 10. 00 am on Friday 28 th November. 1) Print out of final project report 2) Soft copy of project report. 3) Photos and videos

Announcements Guidelines for submission 1) Leaders should get their pen drive to Physics office 2 -422 between 9. 00 – 10. 00 with report + photos + video. Ahmad will copy the files and return your pen drive. 2) Project report file name : group number …final project report. ( eg. Group 10 final project report ; group 15 video ; group 25 photos ) 3) Also submit printed report to Ahmad.

What is a mechanical wave? A mechanical wave: • when a travelling wave, transports and transfers energy not matter; • is produced by a local oscillation, perturbation or disturbance in the material; • requires a medium (e. g. air, water, etc. ) to propagate; http: //www. animations. physics. unsw. edu. au/jw/sound-waves. htm • can be described by Newton’s laws of motion, 4 hence the name “mechanical waves”.

Examples of Mechanical Waves 5

Use of Mechanical Waves Ohmsett Sonic Wave Tank for cleaning oil spills SONAR Speech recognition sound wave patterns 6

Examples of Mechanical Waves SEISMIC WAVES 2011 Japan earthquake 7

Modelling Mechanical Waves Mechanical waves are classified by: Method of energy transmission Transverse: (e. g. string or spring waves); Longitudinal: (e. g. sound waves in water or air). Position of wave action in object Surface: (e. g. small water waves); Body: (e. g. seismic waves). 8

Transverse vs. Longitudinal Waves Transverse Waves Compressions followed by decompressions (rarefactions) that are regularly spaced Direction of vibration of wave front Direction of wave propagation Direction of vibration of particles Direction of propagation 9

Transverse Waves on strings The propagation speed This can be generalized to where T is tension, and μ is mass per unit length (linear mass density) for any type of wave the square of the velocity of waves in an object is equal to the ratio of its elasticity to its inertia 10

Example 1: transverse wave on wire An astronaut on the surface of the Moon wants to know the local g. Moon. He has a 4. 0 m long thin, light wire of mass 5. 0 g, a heavy object of mass 5. 0 kg and a sensitive stopwatch. A pulse travelling along the entire length of the wire returned to the astronaut in ~0. 10 s. How did he calculate g. Moon ? Incident wave pulse 5 kg Returning wave pulse 11

Sound Waves are Longitudinal Waves 12

Sound wave: how it propagates through a row of particles 13

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http: //www. animations. physics. unsw. edu. au/jw/sound-wave-equation. htm 15

Sound wave properties - A longitudinal sound wave consists of alternating high (compressions) and low pressure (rarefactions) regions. Ears detect the pressure differences directly; - The phase difference between particle displacements and pressure or density is 900; - The speed of sound increases with temperature and mass density of material; - Audible Sound: (20 Hz < f < 20 k. Hz). 16

Energy and Intensity of sound waves spherical symmetry 0 d. B (I 0 = 10 -12 W/m 2) Always 17

Human Loudness Perception Thresholds: Hearing (I 0) I 0 = 10 -12 W/m 2 Pain ( I = 1 x 100 W/m 2 ) How “loud” is this painful sound in d. B ? 18

Energy, Intensity and Amplitude Recall that for SHM energy Total Energy = PEMAX = ½k. A 2 so energy is proportional to A 2 - All mechanical waves consist of particles undergoing SHM, and so it can be shown that : For all waves: Intensity is proportional to (Amplitude)2 19

Example 2 – Sound Intensity A loudspeaker can be considered to be a point source of sound creating a spherical sound wave. Here, a loudspeaker has a power of 80. 0 m. W. a) What is the intensity, I, at 3. 0 m from the loudspeaker? b) What is the loudness at 0. 25 m from the loudspeaker? c) Find the change in the intensity level between points located at 0. 10 m and 100. 0 m from the loudspeaker, respectively. 20

Example 3 – Sound Intensity A factory containing 25 identical machines produces an average sound intensity level of 97. 0 d. B just outside the factory. a) What is the total sound intensity outside the factory? b) Calculate the average sound intensity of a single machine; c) How many machines should be removed in order to bring the loudness outside the factory below 90. 0 d. B? 21

Lecture 16 - Mechanical waves READING: Adams and Allday: 6. 2 and 6. 14; Serway and Vuille: 13. 8. 13. 10, 14. 1, 14. 2, 14. 3, 14. 4 and 14. 5. By the end of this lecture you should (be able to): • Define the mechanical wave; • Write an equation for the speed of a transverse wave along a string under a tension, T; • Describe sound as a longitudinal, mechanical wave of pressure; • Know what is meant by a compression and a rarefaction; • Define intensity for a sound wave; • Show that the intensity of spherical sound waves emitted by a point source varies as 1/r 2, where r is the distance from the source; • Calculate the intensity level or loudness in decibels (d. B). 22

Answers to Examples • Example 1 : g. MOON = 1. 6 m/s 2 • Example 2 : (a) I = 0. 71· 10 -3 W/m 2; (b) I = 0. 10 W/m 2; β = 110 d. B; (c) Δβ = 60 d. B. • Example 3 : (a) I = 5. 01· 10 -3 W/m 2; (b) i = 0. 201· 10 -3 W/m 2; (c) at least 20 machines. Additional Resources: Check out these websites What happens when speed ≥ sound speed? http: //www. youtube. com/watch? v=6 o 0 zmafx. Tm. E&feature=related http: //www. youtube. com/watch? v=l. NL 4 HHFG 8 H 4 http: //www. youtube. com/watch? v=q 9 S 0 z 1 ofc. Ic http: //www. youtube. com/watch? v=g. WGLAAYdbbc&feature=related http: //www. youtube. com/watch? v=lboms. OPSSII 23