Waves Start by tapping a pen on the podium, call attention to how often I tap. Part 1

Some basic definitions… Vibration – A “wiggle” in time. Ex. Strike a bell, and the vibrations will continue for some time before they die down. Wave – A “wiggle” in time AND space. Ex. Light and sound are both forms of energy that move through space as waves. Pendulum – An object suspended by a string, that swings back and forth.

Pendulums The time it takes for a pendulum to swing back and forth does not depend on the mass of the pendulum or on the distance that it is swinging. The time of back-and-forth swing – called the period (T) – depends only on the length of the pendulum and the acceleration due to gravity. Measured in seconds. Ex. A longer pendulum has a longer period, which means it swings back and forth more slowly and less frequently than a shorter pendulum.

Parts of a Wave A sine curve is a pictorial representation of a wave. Crest – the high point of a wave. Trough – the low point of a wave Midpoint – an imaginary line halfway between the crest and trough. Amplitude – the distance from the midpoint to the crest (or trough) of the wave. Wavelength – the distance from the top of one crest to the top of the next one.

Frequency Frequency is how often a vibration occurs. Measured in hertz (Hz). 1 Hertz = 1 cycle per second

How are frequency and period related? tapping often = short time between taps high frequency (ƒ) = short period (T) This is called an inverse relationship, as one gets bigger, the other gets smaller. First ask students to talk to their neighbor and discuss how they are related, then ask a group or two to volunteer their answer. Then show the slide. Demonstration: Penulum 1m of string w. large mass at end Relate swing to frequency and period Show how the time is consistent, relate to thier use in clocks, by taking the time of 10 swings LAB #64 Start w/ prelab instructions, then start prelab ƒ= 1 T T = 1 ƒ

Waves The source of all waves is something that vibrates. Energy transferred from a vibrating source to a receiver is carried by a disturbance in the medium, not by matter moving from one place to another within the medium.

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Wave Speed Notes

Discuss with your table… What do you think determines the speed of a wave? The speed of a wave depends on the medium through which the wave moves. Regardless of the medium, the speed, wavelength, and frequency of a wave are all related.

How are period, frequency, & speed related? Remember that speed is distance over time. Wave speed = Since period = Wave speed = wavelength x frequency Or v = λ • f wavelength period 1 frequency

Types of WAves Transverse Wave – A wave where the motion of the medium is at a right angle to the direction in which the wave travels. Longitudinal Wave – A wave where the motion of the medium is along the direction of the wave.

Calculating T & f: Sample Problems A wave has a period of 3 seconds. What is its frequency?

Sample Problems cont… A wave has a frequency of 2 Hz. What is its period?

Waves! amplitude wavelength crest trough Before starting this slide: move a pen up and down on the white board, tracing and retracing a vertical line. Call attention to how frequently I oscillate, relate to frequency. Also discuss the idea of displacement and amplitude (max displacement) Show different frequencies and different amplitudes. Then do the same while walking along the board….WAVES! Show how walking speed and frequency relate to wavelength=== derivation of formula

Longitudinal Vs. Transverse Waves The medium is displaced parallel to the net wave movement Examples: sound, P-waves Sound Wave Animation Transverse: Medium is displaced perpendicular to the net wave movement Examples: Light, radio, x-ray, waves Transverse Wave Animation Say: All waves carry energy, not matter (the medium). But not all waves carry energy in the same way.

Wave speed, frequency, and wavelength are all related! Recall that: speed = distance / time So, wave speed = wavelength / period Or, since frequency = 1 / period : Wave speed = wavelength • frequency v = λ • f

v = wave speed f = frequency λ = wavelength Explain use of variables / symbols to write a general equation. Note that it is a useful short hand way to explain the relationship.

Problem Solving! Follow this 4-step procedure: Identify the given information Pick the appropriate formula(s) Plug in given information Solve & box your answer

Sample Problem The crests on a long surface wave are 20 m apart and have a frequency of 6 Hz. What is the speed of this wave? 1. Identify the given information: λ = 20 m f = 6 Hz v = ? (unknown) 2. Pick the appropriate formula:

3. Plug in given information: v = 20m • 6 Hz 4. Solve v = 120 m • Hz Remember that Hz = 1/s So, v = 120 m/s

Solving for frequency Isolate f Which you can rewrite as:

Solving for wavelength Isolate λ Which you can rewrite as:

Formulas for this unit: ƒ= 1 T T = 1 ƒ