Waves

7A examine and describe oscillatory motion and wave propagation in various types of media 7B investigate and analyze characteristics of waves, including velocity, frequency, amplitude, and wavelength, and calculate using the relationship between wave speed, frequency, and wavelength. SWBAT

What is a wave? Definition: a wiggle in space and time What causes waves? Vibration of molecules Medium: substance that waves travel through. –Waves travel fastest in solids –Waves travel slowest in gas

Transverse Waves waves where particles move perpendicular to the direction of the wave. (ex. ocean waves, light waves, radio)

Longitudinal Waves Wave where particles move along the path of the wave

Basic Wave Properties Amplitude – The height of a wave Wavelength – the distance between crests or compressions Frequency – how often a wave occurs in a time frame (cycles/sec, wiggles/sec, ) Hertz Velocity – how fast a wave can occur in a time span

Amplitude or Height (volume) of crest or trough from NODAL Line, measured in decibels (db) the total energy of the wave

Wavelength Wavelength and frequency are inversely proportional to each other. Longer wavelength / Lower frequency Shorter wavelength / Higher frequency

Parts of a Transverse Wave Node Amplitude Trough Crest Wavelength

Parts of Longitudinal Wave

Which label on the model to the right, represents a wavelength? A.) Q B.) R C.) S D.) T Practice Questions

How to calculate Wave Velocity, Frequency & Period

Frequency The number of wave crests that pass one place each second. (Measured in Hertz) Which wave has a higher frequency? A.A. A.A. B.B. B.B.

Period The time it takes for the back and forth motion. Depends only on the length of pendulum and gravity. (Measured in Seconds)

Frequency & Period Equations Frequency (Hz) = 1 / Period (Second) Period (Seconds) = 1 / Frequency (Hz) What is the frequency in vibrations per second of a 100- Hz wave? The Sears Building in Chicago sways back and forth at a frequency of about 0.1 Hz. What is its period of vibration? A 100-Hz wave vibrates 100 times per second. 1 / frequency = 1vib / 0.1 Hz = 10 seconds

Velocity of a Wave (Wave speed) Velocity = Wavelength x Frequency V = ג x f Velocity = m/s Wavelength ( ג ) = meters Frequency = hertz (cycles/second)

Example 340m/s = λ x 340Hz λ = 1m What is the wavelength of a 340-Hz sound wave when the speed of sound in air is 340m/s?

Problem If a water wave vibrates up and down two times each second and the distance between wave crests is 1.5m, what is the frequency of the wave? What is its wavelength? What is its speed? Frequency = 2Hz Wavelength = 1.5m Wave Speed = λ x f 1.5 x 2 = 3m/s

Problem A wave has a wavelength of 15 cm and has a frequency of 10 waves/second. What is the speed of the wave? Velocity = Wavelength x Frequency V= 15 x 10 V=150 cm/sec

Problem The speed of a wave on a rope is 50cm/s and it’s wavelength is 10cm. What is it’s frequency? Frequency = Wavelength / Velocity F = 10 / 50 F =.2 Hz

Problem A wave is traveling with a velocity of 125m/s and has a frequency of 20 waves/second. What is the length of the wave? Wavelength = Frequency / Velocity Wavelength = 20 / 125 Wavelength =.16 m

What would be the wavelength in centimeters of the wave, illustrated above, if its frequency were doubled? A.) 2.5 B.) 0.8 C.) D.) 0.4 Practice Questions

Harmonics

Harmonic Motion Any repetitive motion Parts: –Cycle – repeated portion of motion –Period – time for one cycle –Frequency – number of cycles per second

Standing Waves When two waves interfere with each other to form one wave. Must have same: Amplitude Wavelength Opposite Direction

Node & Antinode Node – location in rope that remains stationary Antinode – position of largest amplitude

Counting Harmonics

Calculating Harmonics f Hx = f f (X) f f – frequency of fundamental f Hx – frequency of harmonic X – number of harmonic

Examples 1.Find the frequency of the fourth harmonic (h4) of a 6 Hz fundamental. 2.If the eighth harmonic has a frequency of 80 Hz, find the fundamental frequency. f Hx = f f (X) f H4 = (6 Hz)(4) f H4 = 24 Hz f f = f Hx / (X) f f = (80 Hz) / (8) f f = 10 Hz

Wave Interaction

SWBAT 7D investigate behaviors of waves, including reflection, refraction, diffraction, interference, resonance, and the Doppler effect.

Interference When two waves overlap Constructive Interference –When crest meets crest (in-phase) –Results in wave with increased amplitude

Interference Destructive Interference –When crest meets trough (out-phase) –Results in wave with decreased amplitude

Reflection Bouncing back of a wave as it strikes a hard surface.

Diffraction When waves spread out past the edge of a barrier.

Refraction To change the direction of a wave as it passes from one medium to another. (the “bending” of waves)

Sound Waves

Sound Wave (Longitudinal) A slinky is a good example of how compressional waves behave. Sound particles vibrate against one another causing compressions

Origin of Sound Sound is a Longitudinal Wave –Compression & Rarefaction Parts of a Sound Wave Pitch – impression about the frequency –High-pitch = high-frequency –Low-pitch = low-frequency Infrasonic – frequency below 20Hz Ultrasonic – frequency above 20,000Hz

Speed of Sound Sound can be transmitted through solid liquid or gas Speed of sound is ~ 340 meters per second –In air at room temperature –Speed depends on materials elasticity

Question How far away is a storm if you note a 3- second delay between a lightning and the sound of thunder? Speed = Wavelength x Frequency 340m/s = Wavelength x 3s Wavelength = 113m

Sound Terms Forced Vibration – vibration of an object that is made to vibrate by another vibrating object Natural Frequency - frequency at which an elastic object will vibrate Beats – periodic variation in loudness of sound

Resonance Causing another object to vibrate without contact by matching the natural frequency An opera singer can shatter a glass if the singer’s voice matches the natural frequency of the glass

Doppler Effect Apparent change in frequency due to motion of the source

Moving Waves

Types of Waves Seismic Ultrasound Light Sonar Echolocation Sound