Waves and Vibrations Chapter 14 Waves are all

Waves and Vibrations Chapter 14 Waves are all around us in everyday life.

Sound is a Wave.

Radio, TV, and Cell Phones use waves.

Light is a wave. * *But it can act as a particle… another story in Physics!

Main concepts • Types of waves: – Transverse: waves on strings – Longitudinal: sound waves – water waves are more complex (combination) • Relationship of wavelength, frequency and velocity of wave (lf=v) • Wave amplitudes can be added together. • Addition of waves leads to interference: constructive or destructive

Motion of a Transverse Wave on a string • Wave amplitude is y=Asin[2 p(x/l - ft)] • If you sit at one location x, the wave oscillates in time. • If you stop the action at a time t, the wave oscillates as a function of distance x. The wave crest travels a distance l in one period of time, 1/f. Thus the speed is the distance over the time, or lf=v

Motion of Longitudinal Wavelength • Pressure wave • Oscillation of local pressure and gas density

Water waves combine motions Complex motion: combination of transverse and longitudinal motion.

Light & Radio are Electro-magnetic Waves Antenna Electric Field (and Magnetic Field) move TRANSVERSE to direction of propagation of energy. + + + -

Key characteristic of these waves • Energy (in the form of motion) can be transmitted by the wave • The medium (the string, the air, the water) does not move at the speed of the wave—it essentially “stays put” • The energy of the wave is transmitted through the medium from one piece of matter to another • Note that light waves travel without the need for a medium at all!

Demonstrations • • Transverse waves (long spring) Transverse waves (tuning fork) Transverse waves (wave machine) Longitudinal wave/transverse wave (metal rod) • Longitudinal wave (open tube) • Longitudinal wave (recorder)

Superposition (addition) of waves Wave amplitudes are added. They can get larger (constructive) or smaller (destructive) interference when they are superposed.

Wave interference CONSTRUCTIVE DESTRUCTIVE

Demonstrations: waves on a rope. • Reflection of wave at rigid wall • Destructive interference • Standing waves Physlets Illustration 17. 3 superposition of pulses Illustration 17. 4 superposition to make a standing wave. Exploration 17. 4 superposition of two cosine waves to make a standing wave.

Addition of 2 waves that are close in frequency

Beat Frequency

Demonstration • Beat frequency with tuning forks

Standing waves on strings f l=2 L l=L First harmonic Second harmonic 2 f (one octave) l=2/3 L 3 f Third harmonic

Standing waves in columns of air f 3 f 5 f 4 L 4/3 L 4/5 L f 2 L 2 f 3 f L 2/3 L Closed vs. open pipes. The closed pipe has a lower fundamental frequency. The closed pipe has only “odd” harmonics. The open pipe has odd and even. An “octave” is a doubling of the frequency of a note. Our theory predicts a tube will produce a note one octave lower if it is closed off on one end. Try it! A “harmonic” is a multiple of the fundamental frequency, f, 2 f, 3 f, etc.

Intensity of Sound • Our perception of sound is that a sound with 10 times the intensity sounds TWICE as loud • To make it easier to compare sound levels, we use the “decibel (d. B)” scale “Beta” is the “intensity LEVEL”. I is the “intensity”. Be careful. Intensity level (d. B) is dimensionless. Intensity has units of power/area.

Various sound intensities Loudest sound produced in laboratory 109 Saturn V rocket at 50 m 108 Rupture of the eardrum 104 Jet engine at 50 m 10 Threshold of pain Rock concert 120 d. B 110 d. B 1 10– 1 Jackhammer at 1 m 10– 3 Heavy street traffic 10– 5 Conversation at 1 m 10– 6 Classroom 50 d. B 10– 7 Whisper at 1 m 20 d. B 10– 10 Normal breathing Threshold of hearing 10– 11 0 d. B 10– 12

d. B scale of loudness THESE ARE THE SAME: 1. Increase in sound intensity (P/A) of an order of magnitude. 2. Increase in intensity level (d. B) of 10 units. 3. Double the “loudness”.

Intensity vs. distance from a point source Sound is created at origin with power P. It gets spread over the area of an entire sphere of radius R. The sphere area is A=4 pr 2. R 1 P Therefore, the Intensity, P/A, falls off like 1/r 2. R 2

Comparing sound levels • The decibel (d. B) is often used to compare sounds. • The reference intensity, I 0, is the weakest sound that can be heard. Example: A person talking has a sound level of about 50 d. B. What is the sound level of 100 people talking? The intensity level increases 10 d. B for every 10 time increase in intensity.

Fix the noise! • A factory has 50 machines that produce a total of 100 d. B of noise. The Federal standard is that the total must be less than 90 d. B. • How many machines can you operate legally at one time? You must reduce the total noise intensity level by 10 d. B. This means a reduction in noise intensity of a factor of 10. A: You must reduce the number of machines by 10, to 5! Looked at another way….

Adding sound levels • Given that 50 machines produce a d. B level of 100, what is the d. B level of one machine?

Intensity and distance • You are standing 1 meter from a model rocket which takes off producing a sound level of about 85 d. B. What is the sound level 100 meters away? A: Using the 1/r 2 law, the Intensity of the sound (P/A) 100 meters away is 104 times less. This means the sound level is reduced by 40 d. B. The sound level is 45 d. B at 100 meters.