SPH 3UO LESSON PLANS

Text: Physics 11 (Addison-Wesley)

Periodic Motion - motion that repeats itself...each repeated motion is called a cycle.
Types:
1)Transverse - if the object moves perpendicular to its length
ex. water saves, where A is the amplitude and w is the wavelength (sorry, I can't do that symbol)

wavelength (w) = distance between two points vibrating "in phase"...distance from crest to crest or trough to trough
amplitude (A) = maximum distance from the zero point...distance from the zero point to each trough or crest

2) Longitudinal -if the motion of the object is parallel to it's length
ex. .       .      .      .... .        .        .        .       .       .... .    .
                    compression      rarefaction            compression
wavelength goes from compression to compression
T (period): the time for one complete cycle
T= /\t/N       where /\t = time interval in s, N = #of cycles (Hz)
f (frequency): the number of complete cycles in certain time
f = N//\t

The Universal Wave Equation
v= fw...where v = speed (m/s), f = frequency (Hz), w =wavelength (m)
just like d=vt from before

Interference - were particles meet there is a collision, but waves are different
1) constructive interference
-amplitudes add to make a bigger wave
ex.a wave with amplitude  of 3 meets a wave with and amplitude of 5
 ...when they combine the wave has an amplitude of 8, but when the two waves move on they return to their original amplitude
2) Destructive interference
-amplitude add to make a smaller waves
ex. a wave with a negative amplitude of 3 and wave with a positive amplitude of 5 meet
  ...when they collide they result in a positive amplitude of 2, and then both waves return to their original amplitude after they pass
3) Complete destructive Interference...both amplitudes are equal and add to zero
The point of collision that remains at rest the whole time is called the nodal point or node
 

Diffraction...waves tend to spread out after passing through an opening
              ...This effect is maximized if w = d where d is the size of the opening. 
                 If w<<<d then there is not much diffraction.
Refraction...waves travel at different speeds in different mediums.
                  This can cause the wave to change wavelength and sometimes bend.
                  The frequency remains constant.

Example 1: A 17 cm sound wave is moving at 3.4 x 10² m/s.
                 Calculate the frequency and the period of vibration.
Example 2: A wave with a speed of 100 cm/s and a wavelength of 8 cm passes into a second medium in which its speed becomes 60 cm/s.
                 What will be the wavelength of the wave in the second medium?

Speed of Sound... v = 331m/s + 0.59xT in the air (T= temperature in ^oC)
-if the T = 0 ^oC then v_sound faster in warm weather
-speed increases as one moves from gases to liquids to solids (table 7.4, page 278)
Sonar - sound navigation and ranging
measure t (in s for sound to travel out and back), you know v in water at that temperature
use d = vt to find depth of water

Sound- the source of all sound is a vibrating object, and requires a medium to travel through
ex. tuning fork and speaker vibrate to produce longitudinal waves travelling through the air
-sound is the form of energy that can be detected by the human ear
-a healthy young human has an audible range of 16 Hz- 20 kHz

Pitch - depends on the frequency
-high frequency means high pitch
-all frequencies sound different

Intensity (loudness)
-the standard unit for intensity is W/m² but the practical unit is decibel (dB)
-threshold of hearing 0 dB
-threshold of pain 120 dB
These have a difference of 1 000 000 000 000 x
ex. a sound of 50 dB is 10x louder than a 40 dB sound
ex. a sound of 70 dB is 100x louder than a 50 dB sound

ex. speakers...there are nodal lines where the sound waves cancel and there is no sound

Beat frequency...a phenomena that occurs when you hear two notes together that are very close in frequency
You hear (f₁ + f₂)/2 (the average) but the intensity wobbles with a beat frequency of f₁ + f₂
ex. f₁= 500 Hz , f₂= 498 Hz....what do you hear? 499 Hz with a beat frequency of 2 Hz

Standing Waves: If you have a rope that is fixed at both ends, L = length of the rope
f₁  for one loop, f₁ = V/w₁ , w₁ = 2L     ==> f₁ = V/2L
f₂  for two loops, f₂ = V/w₂ , w₂ = L     ==> f₂ = V/L = 2f₁
f₃  for three loops, f₃ = V/w₃ , w₃ = 3L/2     ==> f₃ = 3V/2L = 3f₁
f₈  for eight loops, f₈ = 8f₁
There are the resonant frequencies of the string
The first is called the fundamental frequency
All other are multiples of the fundamental frequency
At any other frequecy you do not get standing waves
When a guitar string is struck it vibrates at the fundamental frequency
f₁ = V/2L
If you want that string to play different f then you can change V or L. L is easier.
ex. A string 20 cm long plays at 392 Hz. How long should it be to produce a 523 Hz note?
f₁ = V/2L find V!
v= f₁ 2L
v = (392)(2)(0.2) = 156.8 m/s, v doesn't change
f₁ = V/2L find L!
523 = 156.8/2L
L = 15 cm