1 VIBRATION AND WAVES Sound and Light

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3 Pendulum

4 Pendulum’s Period: The time required for one complete vibration, for example, from one crest to the next crest, is called the pendulum's period and is measured in seconds. The formula to calculate this quantity is

5 The formula to calculate this quantity is: where L is the length of the pendulum in meters g is the gravitational field strength, or acceleration due to gravitygravitational field strength

6 FREQUENCY: The frequency of a pendulum represents the number of vibrations per second. This quantity is measured in hertz (hz) and is the reciprocal of the pendulum's period.

7 EXAMPLE 1 What Would Be the Period of a Pendulum Located at Sea Level If It Is 1.5 Meters Long?

8 Solution seconds

9 EXAMPLE 2 If the pendulum's length were to be shortened to one-fourth its original value, what would be its new period?

10 SOLUTION Seconds: Since a simple pendulum's period is proportional to the square root of its length cutting the length to one-fourth of its original value would result in the period being reduced to one-half of its original value, or 1.23 seconds.

11 EXAMPLE 3 At sea level, how long would a pendulum be if it has a frequency of 2 Hz?

12 SOLUTION cm

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14 The Sears Building in Chicago sways back and forth at a frequency of 0.1 Hz. What is the period of its vibration? EXAMPLE 4

15 The period is 1/frequency. = 1 vib / 0.1 Hz = 1 vib/0.1vib/sec = 10 sec. EXAMPLE 4

16 TYPES OF WAVES Transverse Wave Longitudinal Wave

17 Longitudinal Wave wave particles vibrate back and forth along the path that the wave travels. Compressional Wave

18 Transverse waves wave particles vibrate in an up-and-down motion.

19 Longitudinal Wave

20 Transverse Wave

21 Wave Speed

22 Wave Speed Speed = Wavelength Frequency

23 Example 5 4. A ruby-throated hummingbird beats its wings at a rate of about 70 wing beats per second. a.What is the frequency in Hertz of the sound wave? b. b. Assuming the sound wave moves with a velocity of 350 m/s, what is the wavelength of the wave?

24 Solution 5: f = 70 Hz and wavelength = 5.0 m

25 Example 6 Ocean waves are observed to travel along the water surface during a developing storm. A Coast Guard weather station observes that there is a vertical distance from high point to low point of 4.6 meters and a horizontal distance of 8.6 meters between adjacent crests. The waves splash into the station once every 6.2 seconds. Determine the frequency and the speed of these waves.

26 Solution 6 The wavelength is 8.6 meters and the period is 6.2 seconds. The frequency can be determined from the period. If T = 6.2 s, then f =1 /T = 1 / (6.2 s) f = Hz

27 Solution 6 Cont’d Now find speed using the v = f wavelength equation. v = f wavelength = (0.161 Hz) (8.6 m) v = 1.4 m/s

28 Example 7 Two boats are anchored 4 meters apart. They bob up and down, returning to the same up position every 3 seconds. When one is up the other is down. There are never any wave crests between the boats. Calculate the speed of the waves.

29 Solution 7 The wavelength must be 8 meters The period is 3 seconds so the frequency is 1 / T or Hz. Now use speed = f wavelength Substituting and solving for v, you will get 2.67 m/s.

30 Wave Interference Constructive And Destructive

31 When the crest of one wave passes through, or is superpositioned upon, the crest of another wave, we say that the waves constructively interfere. Constructive interference also occurs when the trough of one wave is superpositioned upon the trough of another wave. Constructive Wave Interference

32 When the crest of one wave passes through, or is superpositioned upon, the trough of another wave, we say that the waves destructively interfere. During destructive interference, since the positive amplitudes from one crest are added to the negative amplitudes from the other trough, this addition can look like a subtraction. Destructive Wave Interference

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35 Doppler Effect Some Examples

36 When a source of waves and an observer of waves are getting closer together, the observer of the waves “sees” a frequency for the waves that is higher than the emitted frequency. Doppler Effect

37 Conventional Radar All weather radars send out radio waves from an antenna. Objects in the air, such as raindrops, snow crystals, hailstones or even insects and dust, scatter or reflect some of the radio waves back to the antenna. All weather radars, including Doppler, electronically convert the reflected radio waves into pictures showing the location and intensity of precipitation.

38 Doppler Radar Doppler radars also measure the frequency change in returning radio waves.

39 Doppler Effect Wave Barrier Wave Barrier (2D) Shock (3D) Wave

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