Clicker Question

1

The picture shows a representation 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 Question Room Frequency BA

L = 3.75λ = 15λ/4 so λ = 4L/15

2

• CAPA assignment #15 is due on Friday Dec 9th at 10 pm.

• This week: Review in Section, Make-up Labs arranged in other sections. 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

3

• Final Exam is Tuesday morning, Dec 13, 10:30am – 1pm• Exam will be held in Coors Event Center, more details

on Wednesday• Practice Exams and Formula sheet will be posted this

afternoon• Prof. Nagle will hold a review session on Thursday

evening, Dec 8th, 7-9pm, in this room (Duane G1B30).

Final Exam News

4

Two dimensional instrumentsSound also produced by drums! • The vibrations are now of a surface of (usually) circular shape held fixed at the edge.• The allowed standing waves are different!

5

Energy in Sound WavesWaves transmit energy• The rate of energy transport per cross sectional area that the energy is flowing through is called the intensity I.• Intensity is proportional to the square of the amplitude of the wave, just as the energy in a simple harmonic oscillator is proportional to the square of the amplitude.• The units of intensity are Watt/square meter (W/m2).• Loudness is related to intensity but not directly proportional• Human ears can hear sounds from I of 10-12 to 1 W/m2 (without pain)• Human perception of sounds is logarithmic! A factor of 10 in intensity sounds roughly twice as loud

6

Sound Level:

• Because of this perception, we use logarithms to describe the relative sound intensities• 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

7

What is log10(1000)?

A) 100 B) 3 C) 1 D) Need a calculator…

Clicker Question Room Frequency BA

1000 = 103 so log10(1000) = 3

8

What is log10(5 x 107)?

A) log10(5) + 7B) log10(7) + 5C) log10(5) - 7D) Need a calculator…

Clicker Question Room Frequency BA

log10(ab) =log10(a) +log10(b)

9

What is log10(5 x 107)?

A) Between 6 and 7B) Between 7 and 8C) Between 8 and 9D) Need a calculator…

Clicker Question Room Frequency BA

log10(1) = 0 and log10(10) = 1 so log10(5) is a number between 0 and 1

10

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 softer sound intensity andβ2 the louder sound level and β1 the softer sound level.

β2 − β1 = 10log(I2 / I0 ) −10 log(I1 / I0 )

β2 − β1 = 10log(I2 ) −10 log(I0 ) −10 log(I1) +10 log(I0 )

β2 − β1 = 10log(I2 ) −10 log(I1) = 10 log(I2 / I1) = 10 log(2)

β2 − β1 = 10log(2) = 3 dB

11

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) 0.5B) 2C) 4D) 10

Clicker Question 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

12

Sound Wave Interference

• In general, sound waves interfere! Use superposition to add waves• When two single frequency sound waves interfere, a modulation of the amplitude occurs with a frequency called the beat frequency• The beat frequency is the difference between the two interfering frequencies

13

The Doppler Effect

• If something producing a sound is moving relative to something hearing a sound, the heard frequency of the sound shifts!• This shifting is known as the Doppler effect.

14

Doppler Effect Formulas

We have four different simple cases:

fobs =fsource

(1−vsourcevsound

) Source m oving towards stationary oβserver

fobs =fsource

(1+vsourcevsound

) Source m oving away from stationary oβserver

fobs =(1+voβsvsound

)fsource Oβserver m oving towards stationary source

fobs =(1−voβsvsound

)fsource Oβserver m oving away from stationary source

15

Doppler Effect Example

A stationary horn produces a sound at 500 Hz. An observer moving away from the horn at 34 m/s hears what frequency?

fobs =(1−voβsvsound

)fsource Oβserver m oving away from stationary source

fobs =(1−34 m /s340 m /s

)500 Hz = (1−0.1)500 Hz=450 Hz

16

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 matter from their individual random motion!

17

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:

T (oF)=

95T(oC)+ 32

T (K) =T(oC)+273.15