12/5/11 1 1 The picture shows a representa4on of the pressure in a standing sound wave in an organ pipe of total length L. What is the wavelength λ in terms of L? A) λ = 3.75 L B) λ = L/3 C) λ = 4L/15 D) λ = L/4 Clicker Ques,on Room Frequency BA L = 3.75λ = 15λ/4 so λ = 4L/15 • CAPA assignment #15 is due on Friday Dec 9th at 10 pm. • This week: Review in Sec4on, Makeup Labs arranged in other sec4ons. Last chance to make up labs! 5 labs must be completed in order to pass this course. • Prof. Nagle will be out of town Dec 5,6 so his office hours Monday are cancelled, but he is available later in the week if you wish to meet with him. Announcements 2 • Final Exam is Tuesday morning, Dec 13, 10:30am – 1pm • Exam will be held in Coors Event Center, more details on Wednesday • Prac4ce Exams and Formula sheet will be posted this a_ernoon • Prof. Nagle will hold a review session on Thursday evening, Dec 8 th , 79pm, in this room (Duane G1B30). Final Exam News 3 4 Two dimensional instruments Sound also produced by drums! • The vibra4ons are now of a surface of (usually) circular shape held fixed at the edge. • The allowed standing waves are different! 5 Energy in Sound Waves Waves transmit energy • The rate of energy transport per cross sec4onal area that the energy is flowing through is called the intensity I. • Intensity is propor4onal to the square of the amplitude of the wave, just as the energy in a simple harmonic oscillator is propor4onal to the square of the amplitude. • The units of intensity are Wah/square meter (W/m 2 ). • Loudness is related to intensity but not directly propor4onal • Human ears can hear sounds from I of 10 12 to 1 W/m 2 (without pain) • Human percep4on of sounds is logarithmic! A factor of 10 in intensity sounds roughly twice as loud 6 Sound Level: • Because of this percep4on, we use logarithms to describe the rela4ve sound intensi4es • The sound level β for a sound of intensity I is defined using logarithms of base 10: β = 10 log 10 (I/I 0 ) in a unit called decibels (dB). • A decibel is 0.1 bel, but no one uses the bel … • The constant I 0 is a reference intensity of 1.0 x 10 12 W/m 2 • The threshold of hearing is I = 1.0 x 10 12 W/m 2 which is 0 dB • The threshold of pain is about I = 1 W/m 2 , which is 120 dB
Transcript
12/5/11
1
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The picture shows a representa4on of the pressure in a standing sound wave in an organ pipe of total length L. What is the wavelength λ in terms of L?
A) λ = 3.75 L B) λ = L/3 C) λ = 4L/15 D) λ = L/4
Clicker Ques,on Room Frequency BA
L = 3.75λ = 15λ/4 so λ = 4L/15
• CAPA assignment #15 is due on Friday Dec 9th at 10 pm.
• This week: Review in Sec4on, Make-‐up Labs arranged in other sec4ons. Last chance to make up labs! 5 labs must be completed in order to pass this course.
• Prof. Nagle will be out of town Dec 5,6 so his office hours Monday are cancelled, but he is available later in the week if you wish to meet with him.
Announcements
2
• Final Exam is Tuesday morning, Dec 13, 10:30am – 1pm
• Exam will be held in Coors Event Center, more details on Wednesday
• Prac4ce Exams and Formula sheet will be posted this a_ernoon
• Prof. Nagle will hold a review session on Thursday evening, Dec 8th, 7-‐9pm, in this room (Duane G1B30).
Final Exam News
3 4
Two dimensional instruments
Sound also produced by drums! • The vibra4ons are now of a surface of (usually) circular shape held fixed at the edge. • The allowed standing waves are different!
5
Energy in Sound Waves
Waves transmit energy • The rate of energy transport per cross sec4onal area that the energy is flowing through is called the intensity I. • Intensity is propor4onal to the square of the amplitude of the wave, just as the energy in a simple harmonic oscillator is propor4onal to the square of the amplitude. • The units of intensity are Wah/square meter (W/m2). • Loudness is related to intensity but not directly propor4onal • Human ears can hear sounds from I of 10-‐12 to 1 W/m2 (without pain) • Human percep4on of sounds is logarithmic! A factor of 10 in intensity sounds roughly twice as loud
6
Sound Level:
• Because of this percep4on, we use logarithms to describe the rela4ve sound intensi4es • The sound level β for a sound of intensity I is defined using logarithms of base 10: β = 10 log10(I/I0) in a unit called decibels (dB). • A decibel is 0.1 bel, but no one uses the bel … • The constant I0 is a reference intensity of 1.0 x 10-‐12 W/m2 • The threshold of hearing is I = 1.0 x 10-‐12 W/m2 which is 0 dB • The threshold of pain is about I = 1 W/m2 , which is 120 dB
12/5/11
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What is log10(1000)?
A) 100 B) 3 C) 1 D) Need a calculator…
Clicker Ques,on Room Frequency BA
1000 = 103 so log10(1000) = 3
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What is log10(5 x 107)?
A) log10(5) + 7 B) log10(7) + 5 C) log10(5) -‐ 7 D) Need a calculator…
Clicker Ques,on Room Frequency BA
log10(ab) =log10(a) +log10(b)
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What is log10(5 x 107)?
A) Between 6 and 7 B) Between 7 and 8 C) Between 8 and 9 D) Need a calculator…
Clicker Ques,on Room Frequency BA
log10(1) = 0 and log10(10) = 1 so log10(5) is a number between 0 and 1
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Sound Level Example
A loud speaker is adjusted so that it produces a sound of twice the intensity of its original sound. What is the change in sound level?
Let I2 louder sound intensity and I1 the so_er sound intensity and β2 the louder sound level and β1 the so_er sound level.
A 3 dB change in sound level corresponds to a factor of 2 change in intensity. A 6dB change in sound level corresponds to what factor change in intensity (Hint: you don’t need a calculator to answer this!)
A) 0.5 B) 2 C) 4 D) 10
Clicker Ques,on Room Frequency BA
3dB corresponds to a factor of 2; doubling it would be adding it to itself. Using the property of logs, log(a) + log(a) = log(a2), so 22 = 4
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Sound Wave Interference
• In general, sound waves interfere! Use superposi4on to add waves • When two single frequency sound waves interfere, a modula4on of the amplitude occurs with a frequency called the beat frequency • The beat frequency is the difference between the two interfering frequencies
12/5/11
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The Doppler Effect
• If something producing a sound is moving rela4ve to something hearing a sound, the heard frequency of the sound shi_s! • This shi_ing is known as the Doppler effect.
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Doppler Effect Formulas
We have four different simple cases:
fobs =fsource
(1− vsourcevsound
) Source moving towards stationary observer
fobs =fsource
(1+ vsourcevsound
) Source moving away from stationary observer
fobs = (1+ vobsvsound
) fsource Observer moving towards stationary source
fobs = (1− vobsvsound
) fsource Observer moving away from stationary source
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Doppler Effect Example
A sta4onary horn produces a sound at 500 Hz. An observer moving away from the horn at 34 m/s hears what frequency?
fobs = (1− vobsvsound
) fsource Observer moving away from stationary source
fobs = (1− 34 m/s340 m/s
)500 Hz = (1− 0.1)500 Hz = 450 Hz
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What is Temperature?
Temperature is a measure of whether something is hot or cold, but what makes something hot or cold?
Thermal Energy!
But what is Thermal Energy?
Thermal Energy is the KE and PE of the individual atoms in maher from their individual random mo4on!
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How to measure Temperature
• Thermometers are devices which have a measurable property that depends on the thermal energy inside the device. • The most common property is size: most object expand when heated, contract when cooled (not water near freezing point!) • Three main temperature scales: Fahrenheit (°F), Celsius(°C) and Kelvin (K) • Temperatures in Kelvin are called absolute because 0 K means thermal energy is zero • Conversion formulas:
