Day 76, Monday, 4 January, 2016 Waves II Quick review Relationship between SHM and waves Water waves Hertz Wave problems.

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Presentation transcript:

Day 76, Monday, 4 January, 2016 Waves II Quick review Relationship between SHM and waves Water waves Hertz Wave problems

Simple Harmonic Motion becomes a Sine Wave when a Time axis is introduced

Simple Harmonic Motion

If a sine wave has its phase rotated by 90 degrees it becomes a cosine wave. But it is still called a “SINE WAVE” because cosine waves are a subset of sine waves (those that have a phase angle rotation of 90 degrees).

The Pendulum

Forces of gravity and tension on a pendulum T cos Θ = mg

Pendulums have constant frequencies

Formula for the period of a pendulum

Waves Type Transverse, Longitudinal, Surface Amplitude Wavelengthλ PeriodT Frequencyf = 1/T SpeedV = λf

Relationship between SHM and Trigonometry Any Simple Harmonic Motion can be described as sinusoidal motion (a sine wave)

One formula to remember V = λ f  f = V/λ Greek letter “nu” v = frequency Speed of Light (in a vacuum) 3 x 10 8 meters per second nu = c/ λ

1 Formula becomes 6 nu = c/ λ λ = c / nu c = nu λ nu = vel / λ vel = nu/ λ λ = vel / nu EM radiation (light) All other waves replace c with v nu = 1 / T T = 1 / nu

The secret Physicists’ greeting

A wave causes a body to orbit in a circle but not move forward Waves carry energy but not mass

Waves transport energy, not mass

Why waves rise coming into the beach

Water Waves

Hertz The hertz (symbol: Hz) is a unit of frequency. It is defined as the number of complete cycles per second. It is the basic unit of frequency in the International System of Units (SI). Hertz can be used to measure any periodic event; the most common uses for hertz are to describe radio and audio frequencies, sinusoidal contexts in which case a frequency of 1 Hz is equal to one cycle per second.

Practice Problems (old book) P. 335 # 1 a, b, c P. 335 # 6 P. 335 # 7

A sound wave produced by a clock chime is heard 515 m away 1.50 s later: a. What is the speed of sound of the clocks chime in air? b. The sound has a frequency of 436 Hz. What is its period? c. What is its wavelength?

Sound from a clock a. V = d/t v = 515/1.50 = 343 m/s b. P = 1/f = 1/436 = sec = 2.29ms v = c/λ ⇒ freq = speed/wavelength λ = vel/f ⇒ 343.3/436 =.7875 m

Five pulses are generated every s in a tank of water. What is the speed of propagation of the wave if the wavelength of the surface wave is 1.20 cm? speed = ? P =.1000/5 s =.02 s λ = 1.20 cm =.0120 m v = c/λ ⇒ freq = speed/wavelength speed = fλ = (1/P)λ = λ/P =.012/.02 speed =.600 m/s

A periodic longitudinal wave that has a frequency of 20.0 Hz travels along a coil spring. If the distance between successive compressions is m, what is the speed of the wave? λ =.400 m f = 20.0 Hz speed = ? v = c/λ ⇒ freq = speed/wavelength speed = f λ = (20.0)(.400) = 8.00 m/s

Credits Surf picture riverdaughter.wordpress.com/.../ Wave diagram

Credits Unit Circle Graphic html html Wave problems Physics: Principles and Problems by Glencoe Definition of Hertz Wikipedia

Credits II Basic Sine Wave: Simple Harmonic Motion to a Sine Wave graphic: Sine Wave Equation

Credits III Definition of Simple Harmonic Motion Wikipedia Unit Circle Graphic html html

Way More Credits Surf picture Cosine Wave: