Vibrations are the sources of waves. A vibration creates a disturbance in a given medium, that disturbance travels away from the source, carrying

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2 Vibrations are the sources of waves. A vibration creates a disturbance in a given medium, that disturbance travels away from the source, carrying energy with it, we call this traveling disturbance a wave.

3 2 Types of Waves Transverse the source of the disturbance moves perpendicular to the direction of wave motion. Longitudinal- the source of the disturbance moves parallel to the direction of wave motion.

4 Crest peak of a transverse wave Trough lowest point of a transverse wave

5 Compression Place where the medium is pressed together (high density/pressure) Rarefaction Place where the medium is spread apart (low density/pressure)

6 How fast one wave crest (or compression) moves through a medium Speed = Distance Time Symbol: v Measured in meters per second (m/s)

7 Frequency and amplitude are determined by the source. As the wave travels, amplitude decreases, but frequency doesn t change. Wave speed is determined by the medium (more tension or density produces a faster wave). Wave speed is NOT affected by changing the frequency or amplitude. Wavelength is determined by the frequency and wave speed together. Greater frequency means a smaller wavelength. Greater speed means a greater wavelength. Particle speed is determined by the amplitude of the wave and the period of the source

8 Recall that distance traveled is equal to an objects speed*time. Distance = Speed Time D = V t For a wave, the distance it travels during one wave cycle is the wavelength, the time for one wave cycle is the period, so Wavelength = Speed Period λ = v T OR λ = v f

9 A fisherman notices that his boat is moving up and down periodically without any horizontal motion, owing to waves on the surface of the water. It takes a time of 2.4 s for the boat to travel from its highest point to its lowest, a total distance of m. The fisherman sees that the wave crests are spaced a horizontal distance of 5.6 m apart. Determine these waves a) Frequency b) Wavelength c) Amplitude d) wave speed e) average boat speed

10 A transverse wave is traveling on a string. The graph below shows the vertical position of a section of string. a. Determine the frequency of the wave. b. Determine the average speed of a section of string.

11 A wave traveling in the positive x direction with a frequency of 25.0 Hz is shown in the figure below. Find the following values for this wave: a) Amplitude b) Wavelength c) Period d) Speed

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13 When two bumper cars collide, each bounces back in another direction. The two bumper cars cannot occupy the same space, and so they are forced to change the direction of their motion. This is true not just of bumper cars but of all matter. Two different material objects can never occupy the same space at the same time.

14 Because mechanical waves are not matter but rather are displacements of matter, two waves can occupy the same space at the same time. The combination of two overlapping waves is called superposition. Interference When two waves travel through the same space at the same time, they combine briefly to make one wave (called the resultant wave). The resultant wave has an amplitude that is the sum of the amplitudes of the interfering waves.

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16 When two waves on the same side of equilibrium meet The amplitudes of the two individual waves are added together to produce the resultant wave.

17 Destructive interference when two waves on opposite sides of equilibrium meet The amplitudes of the two waves are subtracted to produce the resultant wave.

18 Constructive Interference Total Destructive Interference Partial Destructive Interference

19 Two square wave pulses with amplitudes 15cm and 6cm are moving toward each other. a. What is the maximum amplitude of the resultant wave when the two pulses overlap? Draw the two pulses in this case. b. What is the minimum amplitude of the resultant wave when the two pulses overlap? Draw the two pulses in this case.

20 Draw the resulting wave when these two waves overlap:

21 s/lesson-4/formation-of-standing-waves

22 Standing Wave a wave that is confined in space, caused by interfering identical waves moving oppositely

23 Node- place where the medium doesn t move at all from equilibrium Antinode- place of maximum displacement from equilibrium

24 There must be a node at each end. The string length must be a multiple of ½ wavelength. L = n λ 2L or λ = 2 n Where n is a whole number

25 Fundamental frequency frequency that produces the largest standing wave possible on a string. One antinode. Also called the first harmonic. Wavelength = 2L (where L is the length of the string) Harmonic all possible standing waves. 2 nd harmonic: 2 antinodes, Wavelength = L 3 rd harmonic: 3 antinodes, wavelength = 2 L 3

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27 A guitar string is 0.75 m long. Waves on this string travel at 360 m/s. a. What is the wavelength of the fundamental standing wave? b. What is the frequency of the fundamental? c. What are the wavelength and frequency of the 4 th harmonic? d. If you increase the tension in this string, what happens to the fundamental frequency?