Presentation on theme: "11.7 Properties of Waves – see also lecture notes 11.7"— Presentation transcript:
1 11.7 Properties of Waves – see also lecture notes 11.7
2 Frequency: The number of times the wavelength occurs in one second Frequency: The number of times the wavelength occurs in one second. Measured in kilohertz (Khz), or cycles per second. The faster the sound source vibrates, the higher the frequency.Higher frequencies are interpreted as a higher pitch. For example, when you sing in a high-pitched voice you are forcing your vocal chords to vibrate quickly.
3 Amplitude: The strength or power of a wave signal Amplitude: The strength or power of a wave signal. The "height" of a wave when viewed as a graphHigher amplitudes are interpreted as a higher volume - hence the name "amplifier" for a device which increases amplitude.Sine wave
5 Wavelength: The distance between any point on a wave and the equivalent point on the next phase. Literally, the length of the wave.
6 How are frequency and wavelength related? Electromagnetic waves always travel at the same speed (299,792 km per second). This is one of their defining characteristics. In the electromagnetic spectrum there are many different types of waves with varying frequencies and wavelengths. They are all related by one important equation: Any electromagnetic wave's frequency multiplied by its wavelength equals the speed of light.FREQUENCY OF OSCILLATION x WAVELENGTH = SPEED OF LIGHT
13 Remember the speed of a transverse wave can be calculated using the formula or in a cordThe speed of a longitudinal wave has a form similar to that for a transverse wave.In a long solid rod - where E is the elastic modulus (sec 9.5) and r the material densityIn liquid or gas it is written with b the bulk modulus (sec 9.5) and r the material density
16 Reflection of a eave pulse on a rope lying on a table top Reflection of a eave pulse on a rope lying on a table top. (a) The end of the rope is fixed to a peg. (b) The end of the rope is free to move.
17 When a wave pulse traveling to the right along a thin cord Reaches a discontinuity where the rope becomes thicker andheavier, then part is reflected back and part is transmitted (b)
18 Incident Wave – The wave that strikes a boundary Reflected Wave – The remaining energy not transferredfrom the incident wave that is reflectedback.
22 From low speed to high speed (high density to low density)
23 From high speed to low speed (low density to high density)
24 11.12 Interference; Principle of Superposition Interference – occurs when two waves pass through the same region of space at the same time. The resulting displacement of the waves as they meet is the algebraic sum of their separate displacements.A crest is considered to have a positive value and the trough negative.
25 The Principle of Superposition – can best be described as the overlapping wave that is created when two waves meet.Three types of interference are;a. Constructive Interferenceb. Destructive Interferencec. Partially Destructive
26 Phase – The term phase is used to describe the relative position of the wave crests as they meet. In phase – results in anamplitude that is the sum ofboth crestsb. Out of phase – occurs when thecrests do not meet togetherand the waves partially orcompletely cancel each other.This complete cancellationoccurs when a trough of onewave meets the crest of another.
30 11.3 Standing Wave; Resonance a. Standing wave – produced when twowaves interfere such that theyproduce one large amplitude ofconstructive interference calledthe antinode and areas ofdestructive interference callednodes.b. The nodes and antinodes will remainin fixed positions for a particularfrequency.c. Because standing waves can occur atmore than one frequency, the lowestfrequency give rise to a pattern andare known as the natural frequencyor resonant frequencies of the cord
31 d. Fundamental frequency - corresponds to one antinode note the relationshipof length to wavelength.e. Overtones – are the other naturalfrequencies for the vibrating cord.and are whole number multiples ofthe fundamental frequency and arecalled harmonics.f. In general we can write the equationwhere n = 1,2,3,…g. The integer n labels the number of theharmonic.
32 To find the wavelength,To find the frequency of each vibration , where n = 1,2,3,…To find velocityTo find Force of tension
39 light going from glass to air RefractionOccurs when a wave passes from one region to another where it moves at a different speed e.g.light going from air to glasslight going from air to waterlight going from glass to airwater waves going from deep to shallowsound waves going from air to solid
40 At the interface, the frequency will be the same on both sides and v₁ = f λ₁ v₂ = f λ₂Hence the refracted wave will have a shorter wavelengthObviouslyλ₁ = v₁ λ₂ v₂
41 Note that the refracted wave is bent since the wavelength is decreased so obviously λ₂ = n₁λ₁ n₂ This gives rise to Snell's law, when the wave hits the interface at an angle
42 Wave is incident at θ₁. Refracted wave is at θ₂, what is the relation between θ₁ and θ₂?λ₁ = d sin(θ₁) λ₂ = d sin(θ₂)andn₁λ₁ = n₂ λ₂givingn₁ sin(θ₁) = n₂ sin(θ₂)