Chapter 16 Part 2 PDF

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Chapter 16 Sound and Hearing (Part 2)

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Mi term exam (30th April, Friday) • • • •

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Synchronous (you need to take the exam online at 2pm-2:50pm on 30th April) You will take the mid-term exam in Canvas (don’t need to join any zoom room) “Respondus Lock-down Browser” will be used It means the exam is "open book", but you are not allowed to search answer through internet (although it is unlikely to find similar questions in internet) Equation sheet will be provided (but you can also prepare your own equation sheet) Materials from Ch 12- 15 Multiple choices or answer with number. Total number of question ~ 8-10 questions Review of mid-term on 28th April Sample exam will be uploaded this weekend 2

Sound Waves

• Sound is a longitudinal wave -- it is a wave of compressions and expansions • Sound travels through any matter that is compressible -- sand, steel, the earth, air, water -Chapter 16

Loudness: related to intensity of the sound wave Pitch: related to frequency Audible range: about 20 Hz to 20,000 Hz; upper limit decreases with age Ultrasound: above 20,000 Hz; see ultrasonic camera focusing in following example Infrasound: below 20 Hz https://www.youtube.com/watch?v=uVGG66oF 1v8 Chapter 16

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Wavelength The speed of sound in air is 344 m/s What is the wavelength of the sound with the frequency of middle-C on a piano (262 Hz)? A. 0.38 m B. 0.65 m C.0.76 m D.1.3 m E. 9.0 m

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Example In a liquid with a density of 1000 kg/m3, longitudinal waves with a frequency of 145 Hz are found to have a wavelength of 10.0 m. Calculate the bulk modulus of the liquid.

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Intensity of Sound: Decibels The intensity of a wave is the energy transported per unit time across a unit area. The human ear can detect sounds with an intensity as low as 10-12 W/m2 and as high as 1 W/m2.

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The loudness of a sound is much more closely related to the logarithm of the intensity. Sound level is measured in decibels (dB) and is defined as:

I0 is taken to be the threshold of hearing:

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PhD thesis:

Baby cry: 99-120 dB

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ConcepTes : Decibel Level II A quiet radio has an intensity level of about 40 dB. Busy street traffic has a level of about 70 dB. How much greater is the intensity of the street traffic compared to the radio?

1) about the same 2) about 10 times 3) about 100 times 4) about 1000 times 5) about 10,000 times

ConcepTes : Decibel Level II A quiet radio has an intensity level of about 40 dB. Busy street traffic has a level of about 70 dB. How much greater is the intensity of the street traffic compared to the radio?

1) about the same 2) about 10 times 3) about 100 times 4) about 1000 times 5) about 10,000 times

increase by 10 dB ÞÞ increase intensity by factor of 101

(10)

increase by 20 dB ÞÞ increase intensity by factor of 102 (100) increase by 30 dB ÞÞ increase intensity by factor of 103 (1000)

ConcepTes : Speed of Sound II Do you expect an echo to return to you more quickly or less quickly on a hot day, as compared to a cold day?

1) more quickly on a hot day 2) equal times on both days 3) more quickly on a cold day

ConcepTes : Speed of Sound II Do you expect an echo to return to you more quickly or less quickly on a hot day, as compared to a cold day?

1) more quickly on a hot day 2) equal times on both days 3) more quickly on a cold day

The speed of sound in a gas increases with temperature. This is because the molecules are bumping into each other faster and more often, so it is easier to propagate the compression wave (sound wave).

Conceptual Example: Trumpet players. A trumpeter plays at a sound level of 75 dB. Three equally loud trumpet players join in. What is the new sound level?

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An increase in sound level of 3 dB, which is a doubling in intensity, is a very small change in loudness. In open areas, the intensity of sound diminishes with distance:

However, in enclosed spaces this is complicated by reflections, and if sound travels through air, the higher frequencies get preferentially absorbed.

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Example A baby's mouth is at a distance of 0.25m from her father's ear and a distance of 2.5 m from her mother's ear. What is the difference between the sound intensity levels heard by the father and by the mother ( b father-b mother)?

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How Far Away? Suppose you are 20 m from an alarm emitting sound uniformly in all directions. How far from the alarm do you need to be to reduce the sound level you hear by about 10 dB? A. B. C. D. E.

25 m 30 m 60 m 90 m 200 m

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Sources of Sound: Vibrating Strings and Air Columns Musical instruments produce sounds in various ways— vibrating strings, vibrating membranes, vibrating metal or wood shapes, vibrating air columns. The vibration may be started by plucking, striking, bowing, or blowing. The vibrations are transmitted to the air and then to our ears.

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This table gives frequencies for the octave beginning with middle C. The equally tempered scale is designed so that music sounds the same regardless of what key it is transposed into.

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One String – Many Possible Standing Waves

The Fundamental l1 = 2L

f1 = v/2L

...

… fn = = n f1 nv/2L The Harmonics

ln = 2L/n

Guitar string

The strings on a guitar can be effectively shortened by fingering, raising the fundamental pitch. The pitch of a string of a given length can also be altered by using a string of different density.

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The sound waves from vibrating strings need to be amplified in order to be of a practical loudness; this is done in acoustical instruments by using a sounding board or box, creating a resonant chamber. The sound can also be amplified electronically.

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Wind instruments create sound through standing waves in a column of air.

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Standing Sound Waves s(x,t): P(x,t)

lo

hi

lo

hi

P(x,t):

• Just as with strings, sound waves form nodes and antinodes – Nodes: s(x,t) is zero at a closed end (where air cannot move) – Anti-nodes: s(x,t) is maximum at an open end

• Pressure P(x,t) and displacement s(x,t) are out of phase – at the s(x,t) nodes, pressure is an anti-node (e.g. at closed ends) – at s(x,t) anti-nodes, pressure is a node (e.g. at open ends)

Harmonics in pipes (open end)

ln = 2L/n and fn = nv/2L (ALL n = 1, 2, 3, …).

Harmonics in pipes (close end) •

A closed pipe is usually closed at only one end

ln = 4L/n and fn = nv/4L (ODD n = 1, 3, 5, …).

Mylab and Mastering Homework due Ch 14 – 25th April (this Sunday)

Homework due

Keep reading Ch 16 Sounds and Hearing Prepare your mid-term exam (Ch12-15)

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