LECTURE 7 ENERGY AND INTENSITY. Instructor: Kazumi Tolich

Transcription

1 LECTURE 7 ENERGY AND INTENSITY Instructor: Kazumi Tolich

2 Lecture Energy and intensity Circular, spherical, and plane waves Power, energy, and intensity 15.6 Loudness of sound The decibel scale

3 15.5 Energy and intensity A traveling wave transfers energy from one point to another. The power of the wave is the rate at which the wave transfers energy.

4 15.5 Circular, spherical, and plane waves Circular waves have two-dimensional circular wave fronts. Spherical waves, such as light and sound waves, have three-dimensional spherical wave fronts. A plane wave describes observations of waves far from their source.

5 15.5 Power, energy, and intensity The intensity of a wave is given by I = P a The intensity at distance r from a source radiating uniformly in all directions is given by I = P &'()*+ 4πr.

6 Quiz: Suppose you are standing a distance d away from a speaker that produces sound waves in all direction with a power of P. If the radius of your eardrum is r, what is the intensity of the sound received by the eardrum? A. B. C. D

7 Quiz: answer 7 Suppose you are standing a distance d away from a speaker that produces sound waves in all direction with a power of P. If the radius of your circular eardrum is r, what is the intensity of the sound received by the eardrum? :7; => 7?6;6@A 23 4 would be a correct answer, but P is the power of the source.

8 Quiz: You hear a fire truck with a certain intensity, and you are 1 mile away. Another person hears the same fire truck with an intensity that is about 10 times less. How far is the other person from the fire truck in miles? Assume that the fire truck is a point source.

9 Quiz: answer miles Assuming that the fire truck is a point source, the intensity drops as I = 0 BC@687 DE D 4 = FBC@687 GHI E 4 FBC@687 GHI 4 4 = E 4 = 10 r. = 10r M = 3.2 miles

10 Quiz: (Knight P15.35) 10 LASIK eye surgery uses pulses of laser to shave off tissue from cornea, reshaping it. A typical LASIK laser emits a 1.0-mm-diameter laser beam with a wavelength of 193 nm. Each laser pulse lasts 15 ns and contains 1.0 mj of light energy. What is the power of laser pulse in watts?

11 Quiz: (Knight P15.35) answer 11 LASIK eye surgery uses pulses of laser to shave off tissue from cornea, reshaping it. A typical LASIK laser emits a 1.0-mm-diameter laser beam with a wavelength of 193 nm. Each laser pulse lasts 15 ns and contains 1.0 mj of light energy. What is the power of laser pulse in watts? P = V X = M.Y MY[\ ] M^ MY [_ & = W

12 Quiz: (Knight P15.35) 12 LASIK eye surgery uses pulses of laser to shave off tissue from cornea, reshaping it. A typical LASIK laser emits a 1.0-mm-diameter laser beam with a wavelength of 193 nm. Each laser pulse lasts 15 ns and contains 1.0 mj of light energy ( watts of power). During the very brief time of the pulse, what is the intensity of the light wave in W m.?

13 Quiz: (Knight P15.35) answer 13 LASIK eye surgery uses pulses of laser to shave off tissue from cornea, reshaping it. A typical LASIK laser emits a 1.0-mm-diameter laser beam with a wavelength of 193 nm. Each laser pulse lasts 15 ns and contains 1.0 mj of light energy ( watts of power). During the very brief time of the pulse, what is the intensity of the light wave in W m.? The laser beam is incident on a circular area with a diameter of 1.0 mm, or a radius of 0.50 mm. I = 0 = 0 = e.f MYG g = 8.5 d Y.^Y MY [\ h 4 10MY W m. For fun: This is about 400 million times as intense as the sunlight on earth!

14 Quiz: (Knight P15.34) 14 Solar cells convert the energy of incoming light to electric energy; a good quality cell operates at an efficiency of 15%. Each person in the United States uses energy (for lighting, heating, transportation, etc.) at an average rate of 11 kw. Although sunlight varies with season and time of day, solar energy falls on the United States at an average intensity of 200 W/m 2. Assuming you live in an average location, what total solar-cell area in m 2 would you need to provide all of your energy needs with energy from the sun?

15 Quiz: (Knight P15.34) answer 15 Solar cells convert the energy of incoming light to electric energy; a good quality cell operates at an efficiency of 15%. Each person in the United States uses energy (for lighting, heating, transportation, etc.) at an average rate of 11 kw. Although sunlight varies with season and time of day, solar energy falls on the United States at an average intensity of 200 W/m 2. Assuming you live in an average location, what total solar-cell area in m 2 would you need to provide all of your energy needs with energy from the sun? I = 0 d a = D 7kk78l9:7 = +mmn*n+o*p D 67879:7; = MM MY \ g Y.M^.YY g h 4 = 370 m. Fun fact: the average home size in the US was 2,400 square feet (~220 m. ) for an average of 2.6 people per household in 2010 according to the census.

16 15.6 Loudness of sound You detect sound when a sound wave causes the eardrum to vibrate. Generally, increasing the sound intensity by a factor of 10 results in an increase in perceived loudness by a factor of approximately 2. Hair cells in the cochlea

17 15.6 The decibel scale / Demo 17 Our perception of loudness is given by sound intensity level, β in decibels (db): β = 10 db log MY I I Y I Y is the the threshold of hearing, or faintest sound that can be heard, W/m 2. The sensation of loudness depends on the frequency as well as the intensity of a sound. Human ears are most sensitive at ~4kHz. Demo: Decibel meter

18 Quiz: When his radio breaks, Chuck purchases a new one that produces twice as much acoustic power as the old one. His expectation is that his new radio will sound twice as loud as his old radio. Will he be disappointed? A. Yes, he will be disappointed, the new radio will sound less than twice as loud. B. No, he won t be disappointed, the new radio will sound twice as loud. C. No, he won t be disappointed, in fact the new radio will sound more than twice as loud.

19 Quiz: answer Yes, he will be disappointed, the new radio will sound less than twice as loud. Our perception of loudness varies logarithmically with intensity. Since the new radio produces twice as much acoustic power as the old one, where β old is probably around 110 db.

20 Quiz: You are working in a shop where the noise level is a constant 90 db. Your eardrum has a radius of approximately 4.2 mm. How much power is being received by one of your eardrums?

21 Quiz: answer You are working in a shop where the noise level is a constant 90 db. Your eardrum has a radius of approximately 4.2 mm. How much power is being received by one of your eardrums? β = 10 db log MY D 90 db = 10 db log MY D D 9 = log MY D w 10 y = D D w D w D w I = 10 y I Y = 0 d P = 10 y I Y a = 10 y I Y πr. = 10 y zm. W m. π z{ m. = z W