Waves and Vibrations Chapter 5

Good vibes  A vibration is a motion that repeats back-and-forth about an equilibrium position. Wave - A disturbance transmitted progressively from one place to the next with no actual transport of matter. https://www.youtube.com/watch?v=Eab_beh07HU

Waves and Vibrations What is the relationship between the two?? The source of all waves is something that vibrates. The back-and-forth vibratory motion of a swinging pendulum is called simple harmonic motion. A sine curve is a pictorial representation of a wave.

Parts of a Wave The high points on a wave are called crests. The low points on a wave are called troughs. The term amplitude refers to the distance from the midpoint to the crest (or trough) of the wave. The amplitude is the maximum displacement from equilibrium.

Parts of a Wave The wavelength is the distance between successive identical parts of the wave. The wavelengths of waves at the beach are measured in meters, the ripples in a pond in centimeters, of light in billionths of a meter.

Frequency Frequency - the number of vibrations an object makes in a unit of time (usually one second). A complete back-and-forth vibration is one cycle. If a vibration occurs in one second, the frequency is one cycle per second. The frequency of the vibrating source and the frequency of the wave it produces are the same.

Frequency The unit of frequency is called the hertz (Hz). A frequency of one cycle per second is 1 hertz. Higher frequencies are measured in: kilohertz (kHz—thousands of hertz) megahertz (MHz—millions of hertz) gigahertz (GHz—billions of hertz)

Frequency Electrons in the antenna of an AM radio station at 960 kHz vibrate 960,000 times each second, producing 960-kHz radio waves.

Frequency Period - the time needed to complete one cycle Suppose a pendulum makes two vibrations in one second. Its frequency is 2 Hz and the period is ½ second. Frequency and period are inverses of each other:

Example think! What is the frequency in vibrations per second of a 100-Hz wave? What is the period? Answer: A 100-Hz wave vibrates 100 times/s. The period is 0.01 s.

think! Answer: The period is The Sears Tower in Chicago sways back and forth at a frequency of about 0.1 Hz. What is its period of vibration? Answer: The period is

Wave Motion A wave is a disturbance that moves through matter without displacing any matter. The disturbance moves, not parts of the string itself.

Wave motion Example: Water waves Remember the disturbance moves not the individual droplets.

Wave Speed You can calculate the speed of a wave by multiplying the wavelength by the frequency. If the wavelength is 1 meter, and one wavelength per second passes the pole, then the speed of the wave is 1 m/s.

Wave Speed v = f where v is wave speed,  is wavelength, and f is wave frequency.

Wave Speed of Sound In air, the product of wavelength and frequency is the same for every frequency of sound. That’s why you don’t hear the high notes in a chord before you hear the low notes. The sounds all reach you at the same time. Long wavelengths have low frequencies, and short wavelengths have high frequencies.

Speed of Sound

Types of waves Whenever the motion of the medium is at right angles to the direction in which a wave travels, the wave is a transverse wave.

Types of waves When the particles oscillate parallel to or along the direction of the wave, the wave is a longitudinal wave. Sound travels longitudinally

Interference Waves traveling through the same medium will combine with each other Interference patterns occur when waves from different sources arrive at the same point—at the same time.

Doppler Effect The apparent change in frequency due to the motion of the source (or receiver) is called the Doppler effect. As a wave source approaches, an observer encounters waves with a higher frequency. As the wave source moves away, an observer encounters a lower frequency.

Doppler Effect

Bow wave A bow wave occurs when a wave source moves faster than the waves it produces.

Bow wave

Bow wave The crests overlap at the edges, and the pattern made by these overlapping crests is a V shape, called a bow wave. The same thing happens when an aircraft travels at the speed of sound. The overlapping wave crests disrupt the flow of air over the wings, so that it is harder to control the plane when it is flying close to the speed of sound

Shockwave A shock wave occurs when an object moves faster than the speed of sound. A shock wave is a three-dimensional wave that consists of overlapping spheres that form a cone.

Shockwave The sound of a shockwave is called a sonic boom. The shock wave has not yet encountered listener C, but is now encountering listener B, and has already passed listener A.

Shockwave examples A supersonic bullet passing overhead produces a crack, which is a small sonic boom. When a lion tamer cracks a circus whip, the cracking sound is actually a sonic boom produced by the tip of the whip. Snap a towel and the end can exceed the speed of sound and produce a mini sonic boom. http://www.magellanjets.com/blog/bid/117488/Supersonic-Flight-Faster-Than-Speed-of-Sound https://www.youtube.com/watch?v=BUREX8aFbMs

Sound Waves

Review of Waves Types of waves: Transverse Longitudinal https://www.youtube.com/watch?v=0a5WyAjL1MM Types of waves: Transverse Longitudinal Sound travels as Longitudinal waves

Sound Sound is a form of energy that spreads out through space. All sounds originate in the vibrations of material objects.

I hear voices… The vocal chords in a person’s throat vibrate, causing adjacent air molecules to vibrate. A series of ripples in the form of a longitudinal wave travels through the air. Vibrations in the eardrum send rhythmic electrical impulses into your brain and you hear the voice.

Sound The frequency of the sound waves produced equals the frequency of the vibrating source. Pitch - Our subjective impression about the frequency of sound. A high-pitched sound like that from a piccolo has a high vibration frequency. A low-pitched sound like that from a foghorn has a low vibration frequency.

Sound Frequency A young person can normally hear pitches with frequencies from about 20 to 20,000 hertz. As we grow older, our hearing range shrinks, especially at the high-frequency end. https://www.youtube.com/watch?v=qNf9nzvnd1k

Sound Frequency Sound waves below 20 hertz are called infrasonic. Sound waves above 20,000 hertz are called ultrasonic. Dogs can hear frequencies of 40,000 Hz or more. Bats can hear sounds at over 100,000 Hz.

Power of Sound The Power of Sound: https://www.youtube.com/watch?v=Ude8pPjawKI https://www.youtube.com/watch?v=uPVQMZ4ikvM

Sound wave motion A compression travels along the spring similar to the way a sound wave travels in air.

Sound waves Sound can travel through gases, liquids, and solids The speed of sound differs in different materials. In general, sound is transmitted faster in liquids than in gases, and still faster in solids.

Sound in a vaccuum Sound cannot travel in a vacuum. The transmission of sound requires a medium. There may be vibrations, but if there is nothing to compress and expand, there can be no sound.

Loudness Sound intensity is objective and is measured by instruments. Loudness, on the other hand, is a physiological sensation sensed in the brain. The intensity of a sound is proportional to the square of the amplitude of a sound wave. The unit of intensity for sound is the decibel (dB), after Alexander Graham Bell, inventor of the telephone.

Sound Intensity

Sound Intensity Starting with zero at the threshold normal hearing, an increase of each 10 dB means that sound intensity increases by a factor of 10. A sound of 10 dB is 10 times as intense as sound of 0 dB. 20 dB is not twice but 10 times as intense as 10 dB, or 100 times as intense as the threshold of hearing. A 60-dB sound is 100 times as intense as a 40-dB sound.

Sound Intensity Intensity = 𝑃𝑜𝑤𝑒𝑟 𝐴𝑟𝑒𝑎 Threshold of hearing = 10-12 w/m2 = I0 Threshold of pain = 1 w/m2 To convert to decibals  = 10 log 𝐼 𝐼𝑜

Loudest Stadium The loudest crowd roar at a sports stadium is 142.2 dbA and was achieved by fans of the Kansas City Chiefs (USA), at Arrowhead Stadium in Kansas City, Missouri, USA, on 29 September 2014

Hearing Loss/Damage Hearing damage begins at 85 decibels. The damage depends on the length of exposure and on frequency characteristics. A single burst of sound can produce vibrations intense enough to tear apart the organ of Corti, the receptor organ in the inner ear. Less intense, but severe, noise can interfere with cellular processes in the organ and cause its eventual breakdown. Unfortunately, the cells of the organ do not regenerate.

http://www.chsl.org/soundchart.php

Natural Frequency When any object composed of an elastic material is disturbed, it vibrates at its own special set of frequencies, which together form its special sound. natural frequency - the frequency at which an object vibrates when it is disturbed Depends on: elasticity and shape

Forced sound A forced vibration occurs when an object is made to vibrate by another vibrating object that is nearby. Sounding boards are an important part of all stringed musical instruments because they are forced into vibration and produce the sound.

Resonance If the frequency of a forced vibration matches an object’s natural frequency, resonance dramatically increases the amplitude. An object resonates when there is a force to pull it back to its starting position and enough energy to keep it vibrating. You pump a swing in rhythm with the swing’s natural frequency.

Beats When two tones of slightly different frequency are sounded together, a regular fluctuation in the loudness of the combined sounds is heard. This periodic variation in the loudness of sound is called beats.

Beats The vibrations of the forks will be momentarily in step, then out of step, then in again, and so on. Beat frequency: When one fork vibrates 264 times per second, and the other fork vibrates 262 times per second, they are in step twice each second. A beat frequency of 2 hertz is heard.

Real world example This is how band members tune their instruments: If they hear a beat then the instruments are out of tune. What is the beat frequency when a 262-Hz and a 266-Hz tuning fork are sounded together? A 262-Hz and a 272-Hz?

Assessment Questions The sound waves that humans cannot hear are those with frequencies from 20 to 20,000 Hz. below 20 Hz. above 20,000 Hz. both B and C

Assessment Questions The sound waves that humans cannot hear are those with frequencies from 20 to 20,000 Hz. below 20 Hz. above 20,000 Hz. both B and C Answer: D

Assessment Questions Sound travels in air by a series of compressions. rarefactions. both compressions and rarefactions. pitches.

Assessment Questions Sound travels in air by a series of compressions. rarefactions. both compressions and rarefactions. pitches. Answer: C

Assessment Questions Sound travels faster in a vacuum compared to liquids. gases compared to liquids. gases compared to solids. solids compared to gases.

Assessment Questions Sound travels faster in a vacuum compared to liquids. gases compared to liquids. gases compared to solids. solids compared to gases. Answer: D

Assessment Questions The speed of sound varies with amplitude. frequency. temperature. pitch.

Assessment Questions The speed of sound varies with amplitude. frequency. temperature. pitch. Answer: C

Assessment Questions The loudness of a sound is most closely related to its frequency. period. wavelength. intensity.

Assessment Questions The loudness of a sound is most closely related to its frequency. period. wavelength. intensity. Answer: D

Assessment Questions When you tap various objects they produce characteristic sounds that are related to wavelength. amplitude. period. natural frequency.

Assessment Questions When you tap various objects they produce characteristic sounds that are related to wavelength. amplitude. period. natural frequency. Answer: D

Assessment Questions When the surface of a guitar is made to vibrate we say it undergoes forced vibration. resonance. refraction. amplitude reduction.

Assessment Questions When the surface of a guitar is made to vibrate we say it undergoes forced vibration. resonance. refraction. amplitude reduction. Answer: A

Assessment Questions When an object is set into vibration by a wave having a frequency that matches the natural frequency of the object, what occurs is forced vibration. resonance. refraction. amplitude reduction.

Assessment Questions When an object is set into vibration by a wave having a frequency that matches the natural frequency of the object, what occurs is forced vibration. resonance. refraction. amplitude reduction. Answer: B

Assessment Questions Noise-canceling devices such as jackhammer earphones make use of sound frequency. interference. resonance. amplification.

Assessment Questions Noise-canceling devices such as jackhammer earphones make use of sound frequency. interference. resonance. amplification. Answer: B

Assessment Questions The phenomenon of beats is the result of sound destruction. interference. resonance. amplification.

Assessment Questions The phenomenon of beats is the result of sound destruction. interference. resonance. amplification. Answer: B