SoundProperties and applications

2

The Nature of Waves A wave is a traveling disturbance

two broad classifications of waves, given how the medium (water, ground, air,…) is disturbed

longitudinal: the disturbance is parallel to the direction of motion of the wave (e.g. sound waves; the P or “primary” waves produced by an earthquake—travel the fastest but cause little damage)

transverse: the disturbance is perpendicular to the direction of motion of the wave (e..g a plucked guitar string; the S or “secondary” waves from an earthquake—travel slower that P-waves but cause more damage)

transverse longitudinal

3

The Nature of Waves In some cases

the disturbance can be both transverse and longitudinal, such as in a water wave, or the “Raleigh” wave from an earthquake (it’s a surface wave, and can also be destructive)

The second general property of a wave is that it carries energy

4

Periodic Waves A periodic wave is a wave where the disturbance is cyclic in nature; i.e. the

same patterns repeats over and over.

looking at the shape of the disturbance as a function of distance at some instant in time (figure to the left), we call the length of a single cycle the wavelength of the wave

looking at the disturbance of a specific point over time (figure on the right), we call the amount of time that a complete cycle takes the period T of the wave.

this is the same concept as with simple harmonic motion, and similarly we can define the frequency of the wave as f=1/T

5

The speed of a wave For any periodic wave, there is a

relationship between the speed, wavelength and period (or frequency) of the wave given by

The speed of a wave depends on properties of the medium in which it travels (e.g. density and temperature in air, tension in a string, elasticity in a solid, etc.)

Note: the speed at which particles in the medium move due to the passage of a wave is not the same as the wave speed; in general they don’t even move in the same direction as the wave

fT

v

6

7

8

Sound waves Sound waves in air are longitudinal

waves. The disturbance that propagates in air is a change in the local air pressure (or equivalently density) above or below the average pressure

a region of higher air pressure in the wave is called a condensation, while a region of lower air pressure is called a rarefaction

The speed of sound in air depends on several factors, including the air temperature and pressure. At room temperature and standard atmospheric pressure, the speed of sound is 343 m/s.

Note that the atoms in the air do not move with the velocity v of the sound wave … they just vibrate back and forth as the wave passes

9

10

11

Example The rule of thumb to figure out how far away, in miles, a

thunderstorm is, is to count the number of seconds between seeing a lightning strike and hearing the thunder, and dividing this by 5. Does this work? : a) how far, in miles, does a sound wave in air travel in 5.0s? b) How much time does it take light to cover this distance ? (the speed of light is 3.0x108m/s).

12

Hearing and sound waves The pitch, or tone, of a sound we hear is related to the frequency of the

sound wave: higher frequencies result in a higher pitch

a healthy, young human ear is sensitive to frequencies of around (Audible range) 20hz-20Khz. Infrasonic range includes frequencies less than 20hz

Ultrasonic range includes frequencies greater than 20khz

a pure tone is a sine-wave (so a loudspeaker diaphragm undergoing simple harmonic motion will produce a pure tone), and has a single frequency

most sounds we hear on a day-to-day basis are a combination of many different frequency waves

How loud we perceive a sound to be is related to the amplitude of the sound wave

“A” note : 440hz guitar A-string

13

14

15

16

Sound Intensity the intensity I of a sound

wave is defined to be the power P (work/time) carried by the wave divided by the surface area A through which the wave passes

the SI unit of intensity is therefore W/m2

A

PI

17

Sound Intensity

18

Sound emitted uniformly by a spherical source Consider sound waves that are

emitted from a source with the same intensity in all directions. If the net power of the source is P, then the intensity a distance r away is given by

Intensity that drops off as 1/r2 is a general property of radiation emitted uniformly by a spherical source … eg. light from the sun, radio waves from an antenna, etc.

24 r

P

A

PI

19

20

21

Calculating Decibels The decibel (dB) is a logarithmic unit of measurement that

expresses the magnitude of a physical quantity (usually power) relative to a specified or implied reference level. Its logarithmic nature allows very large or very small ratios to be represented by a convenient number, in a similar manner to scientific notation. Being essentially a ratio, it is a dimensionless unit. Decibels are useful for a wide variety of measurements in acoustics, physics, electronics and other disciplines.

Generally for every factor of 10 change in intensity or dB, there is a factor of 2 change in loudness

dB=10log10 (Is/Io) Is= The intensity of the sound Io= Hearing threshold 1x10-12 W/m2

22

Example

Lightning strikes 500m in the distance, and the subsequent thunder clap is measured to have an intensity of 5.0x10-3 W/m2. Assuming the sound produced by the lightning travels like that from a uniform spherical source, a) What is the sound power of the thunder clap? b) How many decibels does this correspond to?

how far away will the thunder be as loud as a whisper (1.0x10-10 W/m2)? (does this make sense? … what have we missed?)

23

Principle of Linear Superposition When two or more waves are present in the same medium, the

resultant disturbance is the sum of the disturbances from the individual waves

24

Interference when waves are in phase when

they meet, the resultant wave amplitude will be larger than that of the individual components: constructive interference

when waves are out of phase when they meet, the resultant wave amplitude will be smaller than that of the individual components: destructive interference

several phenomena result from this

beat frequencies standing waves

see: http://www.kettering.edu/~drussel/Demos/superposition/superposition.html

interference patterns

25

Interference of two waves sources vibrating in phase

Two wave sources, S1 and S2, are emitting waves in phase, and of exactly the same frequency and amplitude. Consider a point p that is a distance d1 from source 1, and a distance d2 from source 2.

If

where n is a non-negative integer and is the wavelength, then p will be a point of complete constructive interference

If

then p will be a point of complete destructive interference

d1 d 2

p

S1 S2

ndd || 21

2

1|| 21 ndd

26

Example

Consider the configuration of loudspeakers and listener shown to the right. Assume both loudspeakers are playing exactly same music in phase. What set of frequencies will the listener not be able to hear at all?

27

Standing waves Standing waves are waves that look stationary, but have an amplitude that

changes with time. Several situations can produce standing waves, including

the superposition of left and right moving waves on a string

the “natural” modes of vibration of a string fixed at both ends (stringed instruments work like this)

sound waves in a tube open at one or both ends (wind instruments work likes this)

sustained 40mph winds set up standing waves in the Tacoma Narrows Bridge in 1940, causing it to collapse:

28

29

Standing waves on a string fixed at both ends Since both ends of the string are fixed, the only possible

set of wavelengths are

n=1 gives the first or fundamental harmonic n=2 gives the second harmonic or first overtone, n=3 the third

harmonic or second overtone, etc.

Given the relationship f=v, the set of frequencies corresponding to these wavelengths are

nLn /2

L

vnfn 2

30

31

32

33

34

Standing waves in a tube

A resonance can be used to set up standing sound waves in a tube

this is a longitudinal standing wave (compared to the transverse standing wave on a string)

If both ends are open, the possible set of natural frequencies are (as with the string) :

with n=1,2,3,…

L

vnfn 2

35

36

Standing waves in a tube

If only one end is open, the following set of resonant frequencies are possible, though now n can only be an odd integer, n=1,3,5,…

L

vnfn 4

37

38

Example

A tube, open at one end, is cut into two shorter, unequal length pieces. The piece that is open at one end has a fundamental frequency of 675hz, while the piece that is open at both ends has a fundamental frequency of 425hz. What was the fundamental frequency of the original tube?

39

40

41

42

43

44

45

46

47

48

49

50

51

52

Doppler Effect Formula for Sound For waves that travel through a medium (sound, ultrasound, etc...) the relationship

between observed frequency f' and emitted frequency f is given by:

where v is the speed of waves in the medium (in air at T degrees Celsius, this is 331.5 + 0.6T m/s)

vs is the velocity of the source (the thing emitting the sound) or the observer in motionf is the frequency of the sound source f’ is the frequency heard by the observer

53

54

55

56

57