Exam 3 Flashcards
Sound describes
A longitudinal mechanical wave
Sound can’t travel in the absence of
Matter
Speed of sound
The speed of sound is different depending on the material the sound is traveling through. The speed somewhat depends on the temperature
Loudness
Related to the intensity (energy per unit time crossing unit area) in the sound wave
Pitch
Refers to whether the sound is high or low. Frequency determines pitch- the higher the frequency, the higher the pitch.
Audible frequency
20-20,000 Hz, the frequency range that human ears can respond to
Ultrasonic
Waves with frequencies above 20,000 Hz
How are sound waves analyzed based on pressure?
Longitudinal waves are also called pressure waves. Pressure variation can be measured more easily than displacement. In a wave compression where the molecules are close together, pressure is higher than normal. In an expansion (rarefaction) the pressure is less than normal.
Infrasonic waves
Waves less than 20 Hz, or below the audible frequency. Earthquakes are an example. They can cause damage to the human body even though they are inaudible.
Intensity of sound
Defined as the energy transported by a wave per unit time across a unit area perpendicular to the energy flow. Intensity is proportional to the square of the wave amplitude and to the square of frequency. It is inversely proportional to the square of the radius. What we perceive as loudness is not directly proportional to the intensity.
Units of intensity
Decibels- the scale is logarithmic due to the relationship between intensity and loudness.
Sound level
Symbolized by beta- defined in terms of intensity, so units are also decibels. The sound level at the threshold of hearing is 0 dB, so 0 decibels doesn’t equal 0 intensity
Loga-logb equals
Log (a/b)
How does loudness or intensity change the further you get from a sound?
Loudness or intensity decreases the farther you get from a sound. Over long distances, intensity outdoors decreases faster than 1/r squared because some energy is transferred into irregular motion of air molecules. This loss happens more for higher frequencies, so low frequencies are more audible at a distance
How is intensity related to amplitude?
Intensity is proportional to the square of amplitude. It is also proportional to the square of frequency
Speed of sound in air
343 m/s
How does the material affect the speed of sound?
Sound moves slowest in gases and fastest in solids
In what ways do musical instruments produce sound?
Vibrating strings, vibrating membranes, vibrating wood or metal shapes, and vibrating air columns. These vibrations can be produced by plucking, striking, bowing, or blowing.
Acoustic instruments produce sound via
Resonance of standing waves. In instruments like the piano and string instruments, the frequency at which strings vibrate is the same frequency of the sound produced. In wind instruments, sound is produced by the vibrating air column at resonance within the instrument.
Resonant frequency
A natural frequency of vibration determined by the physical parameters of the vibrating object. An object can have multiple resonant frequencies. This is also the frequency at which standing waves are produced in an object
Fundamental frequency
Also called the first harmonic. The lowest resonant frequency that determines the pitch. Corresponds to one antinode (loop) of a standing wave.
Harmonic
An integer (whole number) multiple of the fundamental frequency of a vibrating object. The second harmonic is the first overtone and has twice the frequency of the fundamental.
Overtone
Refers to any resonant frequency above the fundamental frequency - an overtone may or may not be a harmonic. Overtones and harmonics are higher frequency standing waves- they are integer multiples of the fundamental frequency. The second harmonic is the first overtone
String vibration in a string instrument
In stringed instruments, both ends of the vibrating strings are fixed. These fixed locations serve as displacement nodes. The whole string vibrating up and down corresponds to a half wavelength, so the wavelength of the fundamental on the string is equal to twice the length of the string.
Frequency and harmonics in a string instrument
The lowest frequency of resonance is at the fundamental frequency. All other harmonics are at the multiples of the fundamental frequency
How does fingering a string change the frequency?
Fingering a string makes the wavelength shorter, so the frequency is higher. Strings have the same length, but vibrate at a different frequency because they have a different mass per unit length- this effects the velocity of the string
Tube open at both ends
This describes wind instruments. It has pressure nodes and therefore displacement antinodes at the ends. A tube with both ends open has a higher frequency because the wavelength is shorter
Tube closed at one end
Describes some organ pipes. Has a displacement node (and pressure antinode) at the closed end because the air is not free to move.
Tube closed at both ends
This would be useless as an instrument because there’s no contact with open air
Interference
Caused by two or more waves passing through the same region of space simultaneously. Sound waves interfere the same way that other waves do in space
Beats
Waves cause a phenomenon called beats when they interfere in time. Beats are the slow envelope around two waves that are relatively close in frequency. It creates regularly spaced changes in the intensity of sound as the waves are sometimes in phase and sometimes out of phase due to different wavelengths
Doppler effect
When the source of sound is moving toward an observer, the pitch the observer hears is higher than when the source is at rest, and when the source moves away, the pitch is lower. Requires relative motion of the source or observer
Mechanical waves
Oscillations of matter, like water waves and waves on a rope. Waves carry energy from one place to another
Each molecules in a wave oscillates around
An equilibrium point. An object on top of a wave is not carried forward, but moves around an equilibrium point with the motion of the wave.
Pulse
A single wave crest
Continuous/periodic wave
A wave that has an oscillating or vibrating source. The vibration propagates outward and constitutes the wave
Amplitude
The maximum height of a crest or depth of a trough, relative to the level of equilibrium.
Wavelength
The distance between 2 successive crests. Also the distance between 2 successive identical points on the wave
Frequency
The number of crests (complete cycles) that that pass a given point per unit time
Period
The time elapsed between 2 successive crests passing by the same point in space, equals 1/f
Wave speed
The speed at which wave crests move forward
Transverse wave
When the particles of a wave vibrate in a direction perpendicular to the motion of the wave itself
Longitudinal wave
The vibration of particles occurs along the direction of the wave’s motion. They are formed by a spring that is stretched/compressed. Sound waves can be described as longitudinal.
2 types of waves
Mechanical
Electromagnetic
Electromagnetic waves
Transverse waves that don’t require a medium, like light
The angle of reflection equals
The angle of incidence
Principle of superposition
In region where waves overlap, the resultant displacement is the algebraic sum of their separate displacements. A crest is positive while a trough is negative.
Destructive interference
If the two waves have opposite displacements when they overlap, they add to zero
Constructive interference
When two waves overlap and their resultant displacement is greater than either of the individual waves
Phase
Describes the relative positions of the crests of the waves
In phase
When the crests and troughs are aligned for constructive interference
Out of phase
When the crests of one wave meet the troughs of another wave. The crests of one wave occur half a wavelength behind the other wave
Standing wave
When a wave has segments that oscillate up and down in a fixed pattern, but the wave doesn’t travel. It’s equivalent to two traveling waves moving in opposite directions. Can have a fixed end, where the wave pulse inverts and reflects, or a free end
Nodes
In a standing wave, where the segment of the wave remains still at all times (at points of destructive interference. Energy does not flow past nodes
Antinodes
Points of constructive interference in a standing wave, where segments of the wave oscillate with maximum amplitude
Where are standing waves produced?
On strings or on any object that is struck, like a drum membrane or an object made of metal or wood
Refraction
When a 2D or 3D wave traveling in one medium crosses a boundary into a medium where its speed is different, the transmitted wave may move in a different direction than the incident wave. Earthquake waves refract as they pass through layers of rock in the earth
If a wave slows down when passing into a new medium, how does the angle of incidence relate to the angle of refraction?
The angle of refraction is less than the angle of incidence.
How is a magnetic field created?
By a change in the electric field
How is an electric field created?
By a change in the magnetic field
c is equal to
The speed of the wave (light). Velocity is also equal to frequency times wavelength
How do the direction of the electric field and magnetic field compare?
They are perpendicular to each other
How to determine the direction of propagation of a wave
Fingers go in the direction of E and curl in the direction of B. Your thumb points in the direction of propagation.
Gauss’ Law
Relates electric field to its source (electric charge)
Magnetic field lines are
Continuous, they do not begin or end, like electric field lines begin or end on charges
Ampere’s Law
Relates the magnetic field around a current to the current through a surface
Displacement current
Maxwell proposed that the changing electric field between plates is equivalent to an electric current
How are electromagnetic waves produced?
Oscillating (accelerating) charges produce electromagnetic waves. Since a changing electric field produces a magnetic field, and a changing magnetic field produces an electric field, once sinusoidal fields are created they can propagate through space
How are electric and magnetic fields different from static fields?
A static field would extend indefinitely far. Electric and magnetic fields take time to reach distant points. They also store energy, and this energy can’t be transferred to distant points at infinite speed
As the current reverses in an antenna, what happens to the old electric and magnetic field lines?
Old field lines fold back and meet new lines to create closed loops of E fields and B fields. The field near to the antenna is very complex, but the far field has waves that are essentially plane waves
What do EM waves transfer, and in which direction?
They transfer energy in the direction of propagation (motion). The direction is given by the right hand rule. Electric and magnetic waves are perpendicular to each other
How do the magnitude of the E and B fields change with distance?
The magnitude is inversely proportional to distance, so magnitude decreases as distance increases.
Inverse square law
The change in energy carried by EM waves over a distance decreases by 1/r^2
Phase relation of E and B fields
E and B fields are in phase with each other, so they reach their maximums and minimums simultaneously
Why can EM waves propagate in empty space?
EM waves are transverse waves of fields, not of matter like sound is.
Speed of electromagnetic waves in empty space
v=c=E/B
Maxwell’s EM waves are only self sustaining waves if
They travel at a very specific speed (the value of c) through empty space.
Regardless of frequency, all light
Travels at the same speed in a vacuum
Electromagnetic spectrum
Categorizes the wide range of EM frequencies (EM radiation). Includes radio waves, microwaves, infrared light, visible light, UV light, X Rays, and gamma rays (highest frequency)
What does a point on a wave have in common with the wave itself?
It has the same frequency and amplitude as the wave. Changing the amplitude of the wave changes the maximum speed of the point but does not change the speed of the wave
Two waves are traveling toward each other along a rope. What happens when they meet?
They pass through each other due to the principle of superposition. Waves aren’t objects that can collide
What would increase the speed of a wave in a cord?
Stretching the cord further
What direction does a particle on a wave move relative to the wave?
The particle’s direction of velocity will be perpendicular to the direction of the wave’s velocity. The wave has zero velocity at the turning points. If a crest is approaching the particle, the particle will move upward, if not, it will move downward
What happens after waves run into each other, if they come from different directions?
They might have various patterns when they overlap, but each wave continues with its original pattern as it moves away
Does an echo return more quickly on a cold day or a hot day?
On a hot day. The speed of light is not constant, it depends on the temperature.
To make a given sound seem twice as loud, how should a musician change the intensity of the sound?
Increase the intensity by a factor of 10
Octave
A measure of musical frequency. Raising a note by one octave requires doubling the frequency
When a sound wave passes from air into water, what properties of the wave will change?
Wave speed and wavelength. Frequency does not change
A guitar string oscillates. How do the frequency and wavelength change by the time the wave reaches our ears?
The frequency is the same, the wavelength is shorter. As the string oscillates, it causes the air to vibrate at the same frequency. Therefore, the sound wave will have the same frequency as the guitar string. The
speed of sound in air at 20°C is 343 m/s. The speed of sound in the string is the product of the wavelength and frequency, so the sound waves in air have a shorter wavelength than the waves on the string.
Adjacent nodes are separated by
Half a wavelength
In a standing wave, the number of loops corresponds to
The number of the harmonic
Why does a guitar emit a higher pitched note when a string is fretted?
The string vibrates at a higher frequency
If a pipe that was open at both ends now has one end closed off, what happens to the fundamental frequency?
It drops by half. The fundamental wavelength of an open-ended organ pipe is twice the length of the pipe. If one
end is closed, then the fundamental wavelength is four times the length of the pipe. Since the wavelength doubles when one end of the pipe is closed off, and the speed of sound remains constant, the fundamental frequency is cut in half.
A guitar string vibrates at its fundamental frequency. What does this mean?
It means that each small section of the guitar string oscillates up and down at a frequency f. The sound wave created by the vibration propagates through the air with this frequency
Which factors determine the speed of a wave on a string?
The tension and mass of the string
What sound decrease causes a halving of intensity?
3 decibels
Which harmonic frequencies are present in open or closed pipes?
Only odd frequencies are observed in closed pipes, all frequencies are observed in open pipes
In a vacuum, what property do all EM waves have in common?
Velocity
What speed do all EM waves travel at?
The speed of light
Frequency
The number of oscillations made per second
How is radiation intensity related to distance?
Radiation intensity decreases as a square of distance
Direction of the magnetic field in an EM wave
If the intensity of an EM wave doubles, then the electric and magnetic field
Increase by a factor of radical 2
