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Chapter 19 (Vibrations and Waves)

Vibrations

Some Preliminaries Vibration = oscillation = anything that has a back-and-forth to it Eg. Draw a pen back and forth over the same line, repeatedly:When you come back to the same point defines one cycle, one vibrationIf do it faster, your “

frequency

” is higher, your “

period

” is less.

But your “

amplitude

” (max. displacement) is the same – it’s bigger if the

line is bigger. (We’ll come back to these terms shortly) Wave = vibration in both space and time i.e. goes from one place to another: A vibration that

propagates

in space

Clicker Question

Is the time required to swing to and fro on a playground

swing longer or shorter when you stand rather thansit?

A)

Shorter

B)

Longer

C)

The same

Answer: AWhen you stand, the pendulum is effectively shorter,

because the center of mass of the pendulum (you) israised and closer to the pivot. So period is less – ittakes a shorter time.

Wave Description

•^

Simple harmonic motion –

describes pendulum as well as more

general wave-like motion. E.g. a vertical spring with a mass at the end.Hold pendulum bob with ink at the end over a conveyer belt, it traces out

a^

sine wave

(shown here isspring butsameprinciple…)

crests (high points)

troughs (low points)

So:

Amplitude = maximum displacement from equilibrium

(ie to crest or to

trough) , and

Wavelength

crest-to-crest distance

, or, distance btn any

successive identical parts

equilibrium(middle)

Clicker Question

A weight suspended from a spring is seen to bob up and

down over a distance of 20 cm, twice each second.What is its frequency? Its period? Its amplitude?

A)

Frequency 0.5Hz, Period 2s, Amplitude 20cm

B)

Frequency 0.5 Hz, Period 2s,Amplitude 10cm

C)

Frequency 2Hz, Period 0.5s, Amplitude 10cm

D)

Frequency 2Hz, Period 0.5s, Amplitude 20cm

E)

Frequency 2Hz, Period 2s, Amplitude 10cm

Answer C

:^ Frequency = 2 per second = 2 Hz

Period = 1/frequency = ½ sAmplitude = distance from equil to max displacement

i.e. ½ the peak-to-peak distance, i.e. 10cm

Wave motion

•^

Key point is that the

medium

(matter that wave is in) does

not

get

propagated as the wave moves; rather, it is the

disturbance

that

propagates

-^

Eg.

DEMO

: Consider a horizontal rope, with bright marker tied at one

point. Shake it back and forth to generate a wave – notice thedisturbance propagates down rope, but the marker just moves backand forth. Finally, all points return to original position: The disturbance,not the medium, has travelled along.

-^

Via waves, energy can be transferred from a source to a receiver without

-^ the transfer of matter between the two points (eg light waves, sound waves,microwaves…)The larger the amplitude, the more the energy in the wave.

Eg. Water wave: drop stone in a pond. See expanding circles:Water is not transported with the circles – rather, at any point,it moves up and down as wave passes by. (Can see this witha leaf on water’s surface – it just bobs up and down)Again, the medium returns to where it started afterwave has gone by.

Question

If a water wave oscillates up and down two times each

second, and distance between crests is 3 m, what is itsfrequency, wavelength, and speed?Frequency = 2 Hz, Wavelength = 3 m, Speed = 6 m/s

Clicker Question

A mosquito flaps its wings 600 vibrations per second which produces

the annoying 600-Hz buzz. How far does the sound travelbetween wing beats? i.e. calculate the wavelength of themosquito’s sound.

Assume the speed of sound is 340 m/s.A)

600 m

B)

340 m

C)

340 x 600 m = 204 km

D) (340/600) m = 57cmE) (600/340) m = 1.76mAnswer: Dspeed = wavelength x frequency, so wavelength = speed/frequency

= (340 m/s)/(600 Hz)= 0.57 m, or 57cm

Transverse Waves

When medium particles move at

right angles

to the direction of the

disturbance.Eg. Waves on a rope generated by shaking back and forth:Can see this from watching the marker on the earlier demo. Orwatching a leaf on the water’s surface as a water wave passes – itgoes up and down whereas wave is moving radially outward.

Transverse waves include: water waves, waves on a stringedmusical instrument, light, radio waves, microwaves…

Longitudinal Waves

•^

When medium vibrates in the

same

direction as direction of wave travel.

Eg.

Slinky – when push and pull the end away and towards you:

-^

Medium vibrates parallel to direction of wave and energy flow. It’s a compression wave

• distance between compressed regions is wavelength

(or distance between stretched regions)

called

rarefaction

( Note that a slinky also can produce transversewaves. Shake end like:

-^ Longitudinal waves include: sound waves. Air molecs vibrate to andfro. Can also be thought of as a pressure wave.

Standing waves

When forward and backward going waves interfere such that parts of themedium are always stationary. Eg.

Tie rope to a wall and shake. Wave going to wall gets completely reflected. Shake in such a way that set up a standing wave:

Node

= point of zero

displacement Antinode

= regions of max disp.

Are halfway between nodes.

Standing wave DEMO: Tie one end to wall, and shake at right frequency to get (a).Then shake twice as fast, and get (b). Three times as fast, get (c).

Rope length = ½wavelength 1 wavelength and 2 xfreq of (a)

1 ½ wavelengths and 3 xfreq of (a)

• Musical Instruments: work due to standing waves in string, or in airin a pipe in wind instrument. Can determine pitch from length of string,or length of air column… -^ See also simulations http://www.sciencejoywagon.com/physicszone/09waves/

Doppler cont

-^

Nice animation of this at: http://www.sciencejoywagon.com/physicszone/lesson/otherpub/wfendt/dopplerengl.htm

• Doppler effect is why a siren or horn of a car has a higher-than-normal pitch as itapproaches you, and a lower-than-normal pitch as it leaves you: -^ Note:

don’t confuse pitch(=frequency) with loudness(=amplitude)

• Also happens with light – where color is related to frequency, with high frequencybeing towards blue and low frequency is at the red end of spectrumHence, get “blue shift” of an approaching source (freq shifted up); and “red shift” ofreceding source (freq shifted down). Eg.

Distant galaxies show red shift Eg.

Spinning stars – can measure rate by comparing red shift of when it is turning

• Police speed radar operate on the Doppler effect! (see next chap for more)away from us c.f. blue shift of when it turns towards us.

Clicker Question

When an ambulance with its siren on passes you, what

quantities do you measure a change in: Frequency,Wavelength, Wave speed, Amplitude?

A)

All of the above

B)

Frequency only

C)

Frequency and wavelength only

D)

Frequency and wavelength, and, eventually, amplitude

E)

Some other combination

Answer: DFrequency (pitch) and wavelength.Wave speed stays the sameAmplitude (loudness) eventually decreases