Mechanics & Mechanical wave phenomena

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Presentation transcript:

Mechanics & Mechanical wave phenomena Physics 1210 Mechanics & Mechanical wave phenomena Lecture Waves, chapter 15-16

Periodic Motion – Oscillations, SHM

Within the scope of our course, we assume that all HM is well described by sinusoidal type curves (ie cos or sin). The following concepts help to quantify HM: Period T, frequency f, angular frequency w

Analogy sine/circle

Displacement x, velocity v, acceleration a in SHM

Influence of A, k, and m

SHM - Periodic Motion – Energy 

http://www.walter-fendt.de/ph14e/pendulum.htm Simple Pendulum Restoring force follows string angle with normal : Fq directly proportional to q Tangential component acts: Fq = -mg sinq Note that for the SP T does NOT depend on m!

Damped Oscillations

Forced Oscillations Use a periodic force to keep a SHM going against damping. Can also be used to excite the oscillation in cycles to various amplitudes. All bodies have a natural frequency. When they are excited at that f, resonance occurs: A huge change in amplitude

Mechanical Waves Two types of waves Periodicity wave speed, inverse square law Wave equations - Standing waves & normal modes Harmonic motion turns into wave motion when propagating in space

Transverse Waves vs Longitudinal Waves Examples transverse: Light, rope, ocean waves Examples longitudinal: Sound, osc. spring, traffic density 

Wave Characteristics Wave motion can be plotted as function of position x (here: 1d) or time t.

Wave velocity is related to wavelength and frequency.  We can ask about displacement x at a time t.

The Wave Equation: Change of x with t Note: y(x,t) is the wave function not a 2d displacement!

Energy in a Wave  ex.

Boundary Conditions and Superposition http://id.mind.net/~zona/mstm/physics/waves/interference/waveInterference3/WaveInterference3.html

Group task 1: Draw the superposition at t= 4[s], and 6 [s] Group task 2: Which of 1 to 5 is the correct reflection?

Standing Waves When two or more traveling waves pass through a string (medium) a standing (stationary) wave results. No matter how one creates a standing wave on a given piece of string, only certain ‘matching’ waves survive.

Nodes: Nodes - zero displacement Anti-nodes – maxima displacement POSITION OF NODES: At x= 0, l/2, 2l/2, 3l/2, … at x= 0, p/k, 2p/k, 3p/k, … http://mysite.verizon.net/vzeoacw1/harmonics.html

Standing waves possess characteristic fundamental frequencies: How to add the harmonics of a string

Other boundary conditions: One open end

Speed transverse wave

Sound Waves / Longitudinal Waves http://www.physics.smu.edu/~olness/www/05fall1320/applet/pipe-waves.html

Standing Sound Waves, Normal Modes The Kundt Tube experiment:

In continuum mechanics, the bulk modulus B is introduced to describe volume changes in bodies: Since the propagation in the media is different for sound waves, different rules apply for sound speed:

The speed of sound is medium specific: … and not all sounds are audible. A useful concept to analyze waves: The Fourier Transformation complex y/t or p/t data are transformed mathematically into easy to grasp ‘frequency space’ the ear: a natural FT machine

Sound Intensity and the Decibel Scale

Resonance, Interference, Beats Every body has a natural frequency at which it ‘likes’ to vibrate. At this frequency drastic swing amplitudes occur. The phenomenon is called resonance. http://www.walter-fendt.de/ph14e/resonance.htm http://www.ngsir.netfirms.com/englishhtm/StatWave.htm

As two sound waves interfere, a new phenomenon appears: Beats – packets of sounds which give our ear the feeling of distinct sound sections: http://www.mta.ca/faculty/science/physics/suren/Beats/Beats.html They are a result of interference of longitudinal waves. http://www.ngsir.netfirms.com/englishhtm/Beats.htm

The Doppler Effect: When a sound source moves, its wave fronts from the rear arrive delayed at a listeners position: http://lectureonline.cl.msu.edu/~mmp/applist/doppler/d.htm http://library.thinkquest.org/19537/java/Doppler.html

Q16.14 Two vibrating tuning forks have the Group task - Discuss Q16.14 Two vibrating tuning forks have the same f but one is stationary and the other is mounted at the rim of a rotating platform. What does a listener hear? Does it matter where the listener stands?