Properties of waves. Definition:

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1 Properties of waves A wave motion is the ability of transferring energy from one point (the source) to another point without there being any transfer of matter between the two points. Waves are either electromagnetic or mechanical. Electromechanical Waves These types of waves require no medium for propagation; hence they can travel through vacuum. They are often impeded by the presence of matter. Examples include radio waves, light waves and X-rays Mechanical Waves These waves require a material medium in order to transfer energy from source to destination (i.e.: propagation). Examples include water waves, sound waves and waves in stretched string. When a mechanical wave travels from one point to another, it causes each particle inside the medium to oscillate about a fixed point. This oscillation can either be perpendicular to the motion of the wave (Transverse wave) or it can be parallel to the wave (Longitudinal wave). Definition: 1. Transverse waves are waves in which the direction of propagation is perpendicular to the direction of propagation of the wave 2. Longitudinal waves are waves in which the direction of propagation is parallel to the direction of propagation of the wave 3.

2 Below shows an example of a snapshot of a wave ie: Displacement - Position Graph Use of a slinky and an actual diagram of a wave would be beneficial here. Audio visual can be used if no such apparatus exist. Dropping a pebble in a cup would also assist here Reference: A-level physics [Roger Muncaster], fourth edition. Chapter 23 page 422 The diagram above shows the movement of the entire wave as it passes through the water. Let us say we are interested in looking at only one particle as it is affected by the energy coming from the source. The diagram below shows the particle movement of a single water molecule. Displacement - Time graph

3 Definitions 1. Amplitude: The strength or power of a wave signal. The "height" or maximum and minimum displacement of the particle from the rest position. 2. Frequency: The number of times the wavelength occurs in one second. Measured in hertz (Hz), or cycles per second. The faster the sound source vibrates, the higher the frequency. 3. Period: The time required for a particle inside the wave to undergo one oscillation. This is also the time taken for the wave to travel one wavelength. 4. Wavelength: The distance between any point on a wave and the equivalent point on the next phase. Literally, the length of the wave. [Note that this only applies to a wave motion and not a particle inside a wave. Particle movement inside a wave posses a period and NOT a wavelength] 5. Wave Speed (v/c): This is the speed of propagation in a given medium and is given by the formula: v = fλ 6. Displacement: The distance and direction the particle moved due to influence of wave motion. Deriving the Wave Speed of a wave When a pebble is dropped into a bucket of water, as soon as it plunges through the water, it sends ripples across the surface of the water. The ripples move forward at some speed from the source in phase with the energy resonating from the source. This speed is actually referred to as the wave speed of the wave and it can be quantified into a formula: For a wave travelling at a speed (V) the period (T) is the time it takes to complete one complete oscillation/wave length (λ). Now Speed = Distance x Time Therefore: v = λ T alternatively written as v =λ 1 T But f = 1 T Therefore v = f λ

4 Phase of a wave(ϕ) The phase of a wave, measured in radians (this one we will use) or degrees, where 2π degrees is one wavelength, indicates the current position of the wave relative to a reference position. The phase of a point is represented by an angle ϕ. Points on a wave having the same velocity are said to be in phase. where,, and are constant parameters called the amplitude, frequency, and phase of the sinusoid. These functions are periodic with period. The term phase can refer to several different things: It can refer to a specified reference, such as, in which case we would say the phase of is, and the phase of is. It can refer to, in which case we would say and have the same phase but are relative to their own specific references.

5 Phase difference: Phase difference, also called phase angle, in degrees is conventionally defined as a number greater than -180, and less than or equal to Leading phase refers to a wave that occurs "ahead" of another wave of the same frequency. Lagging phase refers to a wave that occurs "behind" another wave of the same frequency. The wave depicted by the dashed line leads the wave represented by the solid line by 90 degrees.

6 Polarization This is a feature of transverse waves ONLY. Transverse waves can either be polarized, unpolarized or partially polarized. Polarization is a property of light wherein some waves are selectively blocked based on the orientations of their electromagnetic oscillation. While polarization is most commonly observed with respect to visible light, microwave light can similarly undergo polarization. This polarization can be demonstrated under proper experimental conditions, even if the microwave light itself is invisible to the human eye. Note, however, that polarization of light is dependent on the wavelength of that light, and therefore materials that polarize visible light will not necessarily polarize microwave light, as microwave light is characterized by much longer wavelengths. Read more: How to Demonstrate the Polarization of Microwaves ehow.com Polarized waves When all vibrations of a transverse wave are in a single plane which contains the direction of propagation of the wave, the wave is said to be plane or linearly polarized. Example of polarizing a wave: Example 1: Light may be polarized by using Polaroid s which contain long parallel molecules. These molecules polarize the light passing through the Polaroid. We can use two sheets of Polaroids to vary the intensity of the light. (See Muncaster pg , section 27.2)

Example 2: Microwaves can be polarized by using a metal grid of parallel bars which are laid out next to each other. Image a page from a note book, the bars resemble this exactly.

7 Example 2: Microwaves can be polarized by using a metal grid of parallel bars which are laid out next to each other. Image a page from a note book, the bars resemble this exactly. When we shine microwaves onto the bars, those waves that are parallel will be filtered, however, those that are perpendicular will be allowed to pass through the grid. The most important issue here is the angle of incidence of the microwave beam. If a wave having an Amplitude of E o is incident on a polarizer such that the angle between the incident and the transmitted E is ϴ. Then the transmitted wave E = E o cosθ and the Intensity (I) = I o cosθ Un-polarized or randomly polarized This occurs because the atoms in a wave do not vibrate in the same direction. The wave therefore is made up of the superposition of a huge number of tiny waves which are in random and uncoralated directions. Examples of this type of wave can be seen in the light given off from an incandescent bulb or thermal radiation. Polarization by reflection (See Muncaster pg )

Waves and Sound. Honors Physics

Waves and Sound. Honors Physics Waves and Sound Honors Physics Simple Harmonic Motion Refers to repetitive, cyclical motion (like a pendulum or waves) Can be described with sine curve For a pendulum only T 2 L g Example problem The world