 Universal Wave Equation. A harp string supports a wave with a wavelength of 2.3m and a frequency of 220.0 Hz. Calculate its wave speed.

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Presentation transcript:

 Universal Wave Equation

A harp string supports a wave with a wavelength of 2.3m and a frequency of Hz. Calculate its wave speed

 A trumpet produces a sound wave that is observed travelling at 350 m/s with a frequency of Hz. Calculate the wavelength of the sound wave.

 Temperature  Linear Density

 What will happen to the wave pulses shown below?  Link to video (blip.tv) Link to video (blip.tv) A: Wave pulse heading towards a wall. B: Wave pulse heading towards a “free end”.

 When a wave moves from one medium to another, its speed changes but its frequency remains the same.  What else happens when waves move from one medium to another? What will happen to the pulses shown below? A: Wave pulse travelling from a thinner rope into a thicker rope. (Less Dense  More Medium, Faster  Slower) B: Wave pulse travelling from a thicker rope into a thinner rope. (More Dense  Less Dense, Slower  Faster)

 Principle of Superposition: The resultant displacement is the sum of the displacements of each component wave.

 What happens after the waves interfere with each other?

 What happens when the wave pulses shown below meet?  Principle of Superposition: The resultant displacement is the sum of the displacements of each component wave.

 Destructive interference: Resultant displacement is smaller than individual pulses.  Constructive interference: Resultant displacement is greater than individual pulses.

 When identical periodic waves travel in opposite directions, they produce a pattern that appears to be standing still. Such waves are known as standing waves. Parts of a standing wave  Nodes  Points on wave that never move  Located half wavelength apart  Antinodes  Points that vibrate maximally

 The standing waves can be produced using one source: a 2 nd identical wave is produced by reflection.  For every medium of fixed length, there are many natural frequencies that produce resonance:

 Fundamental frequency  Lowest natural frequency, longest wavelength  Also called fundamental mode  Overtones  Refer to all natural frequencies higher than the fundamental  1 st overtone = 1 node, etc.  Harmonics  Refer to fundamental & any overtone  Fundamental = 1 st harmonic, 1 st overtone = 2 nd harmonic, etc.

 P. 391 # 1-6

 Reflection  Transmission  Require a medium in which to travel  Interference (Principle of Superposition)  Exhibit constructive & destructive interference What are some other properties of waves?

 The angle of incidence is equal to the angle of reflection: A water wave incident on a barrier. The dotted line is called the “normal”. The normal line by definition is perpendicular to the barrier. All angles are measured from the normal.

 When waves travel from one medium into another, their speed changes.  This causes the wave to bend: When water waves travel from deep to shallow water, the speed of the wave decreases. Since the frequency of waves is constant, because the wave’s speed decreases, its wavelength decreases. (Why?) Waves travelling from a faster to a slower medium always bend towards the normal.

 When waves travel past the edges of a barrier or through a small opening, waves bend & spread:  The amount of diffraction is greatest when the size of the opening is the approx. equal to the wavelength.