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[2p(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 Wave 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 Electric Field (and Magnetic Field) move TRANSVERSE to direction of propagation of energy. + Antenna - - - - - -

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 DESTRUCTIVE CONSTRUCTIVE

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 l=2L f First harmonic l=L 2f Second harmonic (one octave) 3f l=2/3 L Third harmonic

Standing waves in columns of air 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, 2f, 3f, 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 (dB)” scale “Beta” is the “intensity LEVEL”. I is the “intensity”. Be careful. Intensity level (dB) 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 1 Rock concert 10–1 Jackhammer at 1 m 10–3 Heavy street traffic 10–5 Conversation at 1 m 10–6 Classroom 10–7 Whisper at 1 m 10–10 Normal breathing 10–11 Threshold of hearing 10–12 120dB 110dB 50dB 20dB 0dB

dB scale of loudness THESE ARE THE SAME: Increase in sound intensity (P/A) of an order of magnitude. Increase in intensity level (dB) of 10 units. 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=4pr2. Therefore, the Intensity, P/A, falls off like 1/r2. R1 P R2

Comparing sound levels The decibel (dB) is often used to compare sounds. The reference intensity, I0, is the weakest sound that can be heard. Example: A person talking has a sound level of about 50 dB. What is the sound level of 100 people talking? The intensity level increases 10 dB for every 10 time increase in intensity.

Fix the noise! A factory has 50 machines that produce a total of 100 dB of noise. The Federal standard is that the total must be less than 90 dB. How many machines can you operate legally at one time? You must reduce the total noise intensity level by 10 dB. 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 dB level of 100, what is the dB 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 dB. What is the sound level 100 meters away? A: Using the 1/r2 law, the Intensity of the sound (P/A) 100 meters away is 104 times less. This means the sound level is reduced by 40 dB. The sound level is 45 dB at 100 meters.