Vibrations and Waves
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Transcript of Vibrations and Waves
Vibrations and Waves
Eleanor Roosevelt High SchoolChin-Sung Lin
Lesson 22
Vibrations and Waves
What is Vibrations?
What is Vibrations?
Vibrations
Vibration: A wiggle in time is a vibration
A vibration cannot exist in one instant, but needs time to move back and forth
Mechanical oscillations about an equilibrium point
Vibrations
Period (T): The amount of time required for a vibrating particle to return to its original position (one cycle). A complete back-and-forth vibration is one cycle. The unit of period is second (s)
Vibrations
Frequency (f): The number of back-and-forth vibrations it makes in a given time. The unit of frequency is called hertz (Hz). One Hz is one cycle or vibration per second
Frequency
Frequency unit: 1 kilohertz (kHz— thousands of hertz) = 1 x 103 Hz
1 megahertz (MHz— millions of hertz) = 1 x 106 Hz
1 gigahertz (GHz— billions of hertz) = 1 x 109 Hz
frequency = 1/period and period = 1/frequency
f = 1/T and T = 1/f
Frequency Example
If an electromagnetic wave has frequency 5.0 x 106 Hz, what is the period of the wave? What type of wave is that?
Frequency Example
If an electromagnetic wave has period 2.0 x 10-
9 s, what is the frequency of the wave? What type of wave is that?
Frequency
High frequency and low frequency
What is Wave?
Waves
sound waves
light waves
radio waves
microwaves
water waves
stadium waves
earthquake waves
rope waves
slinky waves
Waves
Wave: A wiggle in space and time is a wave
A wave cannot exist in one place, but must extend from one place to another
Disturbances that transfer energy from one place to another
Waves
Crest and Trough: The high points of a wave are called crests, and the low points of a wave are called troughs
Waves
Amplitude (A): refers to the distance from the midpoint to the crest (or trough) of the wave. So the amplitude equals the maximum displacement from equilibrium
Waves
Wavelength (λ): The distance between successive identical parts of the wave such as from the top of one crest to the top of the next one
Waves
TimeAmplitude
Period
Crest
Trough
DistanceAmplitude
Wavelength
Vibration
Wave
Aim: Speed of WavesDoNow:
Non-digital clocks have a second hand that rotates around in a regular and repeating fashion. The frequency of rotation of a second hand on a clock is _______ Hz
An echo (reflection of the scream off a nearby canyon wall) is heard 0.82 seconds after the scream. The speed of the sound wave in air is 342 m/s. Calculate the distance from the person to the nearby canyon wall
Aim: Speed of WavesDoNow:
Non-digital clocks have a second hand that rotates around in a regular and repeating fashion. The frequency of rotation of a second hand on a clock is __1/60__ Hz
An echo (reflection of the scream off a nearby canyon wall) is heard 0.82 seconds after the scream. The speed of the sound wave in air is 342 m/s. Calculate the distance from the person to the nearby canyon wall __ 140 m__
Speed of Waves
Waves
wave speed = wavelength x frequency
= wavelength / period
v = f = / Twhere v is the wave speed [m/s]
is the wavelength [m]
f is the wave frequency [Hz]
T is the wave period [s]
This relationship holds for all kinds of waves
Waves
The long wavelengths have low frequencies; the shorter wavelengths have higher frequencies
Wavelength and frequency vary inversely to produce the same speed for all waves
Wave Example
The time required for the sound waves (v = 340 m/s) to travel from the 512-Hz tuning fork to 20 m away is?
Wave Example
The time required for the sound waves (v = 340 m/s) to travel from the 512-Hz tuning fork to 20 m away is?
[0.059 s]
Wave Example
Mac and Tosh are resting on top of the water near the end of the pool when Mac creates a surface wave. The wave travels the length of the pool and back in 25 seconds. The pool is 25 meters long. Determine the speed of the wave.
Wave Example
Mac and Tosh are resting on top of the water near the end of the pool when Mac creates a surface wave. The wave travels the length of the pool and back in 25 seconds. The pool is 25 meters long. Determine the speed of the wave.
[2 m/s]
Wave Example
The water waves travel at a speed of 2.5 m/s and splashing periodically against Wilbert's perch. Each adjacent crest is 5 meters apart. The crests splash Wilbert's feet upon reaching his perch. How much time passes between each successive drenching?
Wave Example
The water waves travel at a speed of 2.5 m/s and splashing periodically against Wilbert's perch. Each adjacent crest is 5 meters apart. The crests splash Wilbert's feet upon reaching his perch. How much time passes between each successive drenching?
[2 s]
Wave Example
A ruby-throated hummingbird beats its wings at a rate of about 70 wing beats per second. (a) What is the frequency in Hertz of the sound wave? (b) Assuming the sound wave moves with a velocity of 350 m/s, what is the wavelength of the wave?
Wave Example
A ruby-throated hummingbird beats its wings at a rate of about 70 wing beats per second. (a) What is the frequency in Hertz of the sound wave? (b) Assuming the sound wave moves with a velocity of 350 m/s, what is the wavelength of the wave?
(a) [70 Hz]
(b) [5 m]
32
Wave Example
Two boats are anchored 4 meters apart. They bob up and down, returning to the same up position every 3 seconds. When one is up the other is down. There are never any wave crests between the boats. Calculate the speed of the waves.
Wave Example
Two boats are anchored 4 meters apart. They bob up and down, returning to the same up position every 3 seconds. When one is up the other is down. There are never any wave crests between the boats. Calculate the speed of the waves.
[2.667 ms]
Wave Example
If an electromagnetic wave has period 4.0 x 10-15 s, what is the frequency of the wave? What is the wavelength of the wave? Which type of wave is that?
Aim: Types of WavesDoNow: If an electromagnetic wave has period 4.0 x 10-15 s,
what is the frequency of the wave? What is the wavelength of the wave? Which type of wave is that?
Aim: Types of WavesDoNow: If an electromagnetic wave has period 4.0 x 10-15 s,
what is the frequency of the wave? What is the wavelength of the wave? Which type of wave is that?
(a) [2.5 x 1014 Hz]
(b) [1.2 x 10 -6]
(c) Infrared
Types of Waves
Transverse Waves
Transverse Waves
Whenever the motion of the medium is at right angles to the direction in which a wave travels
Longitudinal Waves
Longitudinal Waves
Whenever the particles of the medium moves back-and-forth along the direction of the wave rather than at right angles to it
Combination of Waves
Combination of Transverse & Longitudinal Waves
Water waves are an example of a combination of both longitudinal and transverse motions. The particles travel in clockwise circles
Longitudinal or Transverse?
Interference
Interference
More than one vibration or wave can exist at the same time in the same space
Interference
The principle of superposition of waves states that the resultant displacement at a point is equal to the vector sum of the displacements of different waves at that point
Constructive Interference
The two waves are in-phase with each other they add together
Constructive Interference
The two waves are in-phase with each other they add together
Destructive Interference
The two waves are 180° out-of-phase with each other they cancel
Destructive Interference
The two waves are 180° out-of-phase with each other they cancel
Interference Patterns
Two waves overlap each other will form an interference pattern
Interference Patterns
Gray “spokes”: zero amplitude
Dark- & light-striped: crests of one wave overlap the crests of another, and the troughs overlap as well
Reflection of Waves
Reflection from a Fixed Boundary: at a fixed boundary, the displacement remains zero and the reflected wave changes its polarity
Reflection of Waves
Reflection from an Open Boundary: at a free (soft) boundary, the restoring force is zero and the reflected wave has the same polarity as the incident wave
Standing Waves
A standing wave may be created from two travelling waves with the same frequency (wavelength), the same amplitude, and are travelling in opposite directions in the same medium
Standing Waves
The nodes are stable regions of destructive interference and remain stationary
The positions with the largest amplitudes are known as antinodes. Antinodes occur halfway between nodes
Standing Waves
Various standing waves can be produced by increasing the frequency of vibrating string
The wavelengths and frequencies of standing waves are:
Standing Waves
Standing Waves
The frequencies of the standing waves on a particular string are called resonant frequencies
They are also referred to as the fundamental and harmonics
Standing Waves Standing waves can be produced in either transverse
or longitudinal waves Various standing waves with open ended, close 1 end,
and close 2 ends
Doppler Effect
Doppler Effect
The Doppler effect is the perceived change in frequency of wave emitted by a source moving relative to the observer
Doppler Effect
When a wave source create ripple at a fixed position and at constant frequency the crest of the wave are concentric circles the distance between wave crests (wavelength) will be the
same the wave speed is the same in all directions the frequency of wave motion at point A and B are the
same
A
B Wavelength
Doppler Effect If the wave source moves across the water at a speed less
than the water speed, the wave motion at point A would be at higher frequency than point B
The greater speed of the source, the greater will be the Doppler effect
The Doppler effect is about the change of the perceived frequency of the wave, not the change of wave speed
A B
Long WavelengthShort Wavelength
Doppler Effect Application
Blue Shift: Light source approaches, frequency increases Red Shift: Light source recedes, frequency decreases A measurement of this shift enables astronomers to
calculate stars’ speeds of approaching or recession
Doppler Radar
Doppler Radar
Bow Waves & Shock Waves
Bow Waves
v = 0 v < vw
Bow Waves
v = 0 v < vw
v = vw
Bow Waves
v = 0 v < vw
v = vw v > vw
Bow Waves
v = 0 v < vw
v = vw v > vw
Bow Waves
v = 0 v < vw
v = vw v > vw
Bow Waves
When the source moves the same speed of the waves, the waves pile up and the overlapping wave crests disrupt the flow of air
When the source moves faster than the wave speed, the overlapping crests create a V shape, called a bow wave
The greater the moving speed produces a narrower V shape
An airplane can become supersonic and fly into smooth and undisturbed air because no sound wave can propagate out in front of it
Bow Waves
Shock Waves A speedboat generates a 2-D bow wave A supersonic aircraft generates a 3-D shock wave The conical shell of compressed air that sweeps behinds
a supersonic aircraft is called a sonic boom. The high-pressure sound due to the overlapping crests has much the same effect as an explosion
Shock Waves
Shock Waves
Shock Waves
The End