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VIBRATION AND WAVES Sound and Light

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Pendulum

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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

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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 gravity

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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.   

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EXAMPLE 1

What Would Be the Period of a Pendulum Located at Sea Level If It Is

1.5 Meters Long?

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Solution 1

2.46 seconds

 

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EXAMPLE 2

If the pendulum's length were to be shortened to one-fourth its

original value, what would be its new period?

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SOLUTION 21.23 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.

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EXAMPLE 3

At sea level, how long would a pendulum be if it has a frequency of 2

Hz?

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SOLUTION 3

6.21 cm

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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

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The period is 1/frequency.

= 1 vib / 0.1 Hz = 1 vib/0.1vib/sec =

10 sec.

EXAMPLE 4

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TYPES OF WAVES

• Transverse Wave

• Longitudinal Wave

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

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Transverse waveswave particles vibrate in an up-and-down motion.

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Longitudinal Wave

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Transverse Wave

http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=14.0

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Wave Speed

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Wave Speed

Speed = Wavelength • Frequency

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Example 54. 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?

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Solution 5:

f = 70 Hz and

wavelength = 5.0 m

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Example 6Ocean 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.

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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 = 0.161 Hz

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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

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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.

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Solution 7

The wavelength must be 8 meters

The period is 3 seconds so the frequency is 1 / T or 0.333 Hz.Now use speed = f • wavelength Substituting and solving for v, you will get

2.67 m/s.

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Wave Interference

Constructive

And

Destructive

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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

http://id.mind.net/~zona/mstm/physics/waves/interference/constructiveInterference/InterferenceExplanation2.html

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• 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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Doppler Effect

Some Examples

http://www.wfu.edu/physics/demolabs/demos/3/3b/3B40xx.html

http://www.walter-fendt.de/ph11e/dopplereff.htm

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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

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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.

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Doppler Radar

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

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Doppler EffectWave

BarrierWave

Barrier (2D)Shock (3D)

Wave

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