Vibrations and Waves Eleanor Roosevelt High School Chin-Sung Lin Lesson 22

Vibrations and Waves

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 10 3 Hz  1 megahertz (MHz— millions of hertz) = 1 x 10 6 Hz  1 gigahertz (GHz— billions of hertz) = 1 x 10 9 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 10 6 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 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 Time Amplitude Period Crest Trough Distance Amplitude Wavelength Vibration Wave

Aim: Speed of Waves DoNow:  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 Waves DoNow:  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 = / T where 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 s, what is the frequency of the wave? What is the wavelength of the wave? Which type of wave is that?

Aim: Types of Waves DoNow:  If an electromagnetic wave has period 4.0 x s, what is the frequency of the wave? What is the wavelength of the wave? Which type of wave is that?

Aim: Types of Waves DoNow:  If an electromagnetic wave has period 4.0 x 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 Hz] (b) [1.2 x ] (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

 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

 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

 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 Wavelength Short 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

Bow Waves & Shock Waves

Bow Waves v = 0 v < v w

Bow Waves v = 0 v < v w v = v w

Bow Waves v = 0 v < v w v = v w v > v w

Bow Waves v = 0 v < v w v = v w v > v w

Bow Waves v = 0 v < v w v = v w v > v w

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

The End