Waves and Sound

Question 1

Wave

Answer 1

A disturbance in some medium in which the parts of the medium are displaced and the displacement changes with time due to interactions between the parts

Question 2

Travelling wave

Answer 2

A disturbance that travels in some direction with a particular speed

Question 3

Transverse wave

Answer 3

A wave in which the displacement is perpendicular to the direction of travel of the wave
- wave on a string
- wave on water

Question 4

Longitudinal wave

Answer 4

A wave in which the displacement is in the same direction that the sound wave is travelling in
- slinky waves
- sound waves

Question 5

Snapshot graph

Answer 5

Shows the displacement as a function of the position along the wave at a specific time

Question 6

History graph

Answer 6

Shows the displacement at one location as a function of time

Determines the sound that we hear (the sound wave at the location of our ear)

Question 7

Sinusoidal waves

Answer 7

Waves with a sinusoidal shape (history graph)
Caused by simple harmonic oscillations

Question 8

Wavelength of a sinusoidal wave

Answer 8

The distance in space between neighbouring peaks

Question 9

Frequency/period of a sinusoidal wave

Answer 9

The frequency/period of oscillation for any point on the wave

Question 10

Wave speed

Answer 10

The rate at which the features of a wave travel in the direction that the wave is moving

Question 11

How are wavelength, frequency/period, and wave speed related?

Answer 11

Question 12

Pressure

Answer 12

In a gas, the force that it exerts per unit of area

Measured in Pascals
1 Pascal = 1 Newton per square metre

Question 13

Standard atmospheric pressure

Answer 13

100,000Pa / 100kPa

Question 14

Force of a gas on a surface

Answer 14

F = P A

Force, pressure, area

Question 15

Density of molecules & pressure

Answer 15

Molecules per unit volume

Pressure is proportional to density of molecules (for a fixed temperature)

Question 16

How does a microphone work?

Answer 16

A membrane vibrates in response to the changes in pressure caused by a sound wave

The microphone converts the displacement of the membrane as a function of time to a recordable electrical signal

Question 17

How does a speaker work?

Answer 17

A speaker converts electrical signals into the motion of an object that displaces the air molecules to create a sound wave

Question 18

The principle of superposition

Answer 18

Multiple sound waves can travel in the same medium without disturbing each other

The net displacement due to a combination of waves is the sum of the displacements that each wave would have individually

Question 19

Fourier’s theorem

Answer 19

Any periodic time graph can be decomposed as a sum of sinusoidal time graphs with frequencies f, 2f, 3f, 4f, etc.

Any musical tone (f) is equivalent to a combination of pure tones with frequencies f, 2f, 3f, 4f, etc.
f: the fundamental
2f: the second harmonic
3f: the third harmonic

Question 20

What is the difference between musical and non-musical sounds?

Answer 20

Non-musical sounds can also be understood as a combination of pure tones, but they generally involve a wide range of frequencies

Question 21

Spectrum

Answer 21

The information about the pure-tone frequencies present in a sound and the amount of each

Question 22

Spectrum graph

Answer 22

Shows the amplitude of each frequency of pure tone present in a sound

Question 23

Standing wave

Answer 23

A combination of a travelling sinusoidal wave moving to the left and a travelling sinusoidal wave with the same wavelength moving to the right, superimposed

Has a sinusoidal shape which simply oscillates up and down
Nodes and antinodes remain in the same place

Question 24

Nodes

Answer 24

Constant places in a standing wave with zero displacement (while rest of wave oscillates up and down)

On a stretched string fixed at both ends, a node must be at both ends
- allowed wavelengths are 2L, L, 2L/3, L/2, etc. (2L divided by any whole number)

In a cylindrical tube, closed ends have a node, and open ends have an antinode

Question 25

Antinodes

Answer 25

Constant places in a standing wave with maximum displacement (while rest of wave oscillates up and down)

In a cylindrical tube, closed ends have a node, and open ends have an antinode

Question 26

Wavelengths in a closed-open tube

Answer 26

In a cylindrical tube, closed ends have a node, and open ends have an antinode

4L, 4L/3, 4L/5, etc.

Question 27

Wavelengths in an open-open tube

Answer 27

In a cylindrical tube, closed ends have a node, and open ends have an antinode

2L, 2L/3, L/2, etc.

Question 28

How does hearing work?

Answer 28

Pressure variations in sound waves vibrate the eardrum

The eardrum transfers vibration to the ossicles

Vibration is transformed into waves in the fluid and basilar membrane of the cochlea

Each frequency resonates on a specific area of the basilar membrane, sending signals to specific nerve cells

The nerve cells that fire and their rate of firing (caused by amplitude) determine the information that the brain recieves about the spectrum of sound

Question 29

What range of frequencies can the human ear detect?

Answer 29

20Hz - 20,000Hz

Question 30

Just noticable difference in frequencies

Answer 30

The minimum amount of change required to be detected 50% of the time

1/2 semitone (lower frequencies) to 1/20th of a semitone (higher frequencies)

Question 31

Intensity

Answer 31

Measures the amount of energy per time that flows through a unit of area perpendicular to the sound wave

Watts per square metre

Proportional to the square of the amplitude

Question 32

Volume

Answer 32

Measured by the amplitude of displacement of the air, the size of pressure variations in the wave, or the intensity of the sound wave

Question 33

Decibel scale

Answer 33

Describes sound intensities relative to the quietest sound we can typically hear (0dB)

+10dB = 10x increase in intensity
+20dB = 100x increase in intensity

Question 34

Loudness

Answer 34

Subjective perception of volume

Each 10dB increase in intensity is perceived as 2x increase in loudness

For a fixed intensity, perceived loudness depends on frequency
- more intensity required at high or low frequencies to produce the same loudness
- ears are most sensitive around 3000Hz (the fundamental resonant frequency of the ear canal, open-closed tube)

Question 35

Constructive interference

Answer 35

Two pure tones with the same frequency and amplitude will reinforce each other if oscillating together (in phase)

Question 36

Destructive interference

Answer 36

Two pure tones with the same frequency and amplitude will cancel each other out if oscillating oppositely (out of phase)

Question 37

Beat frequency

Answer 37

The difference in the frequency of two pure tones with slightly different frequencies

The two tones will alternate between oscillating in phase and out of phase (reinforcing and cancelling); we perceive this as a single frequency whose loudness varies periodically

Question 38

The limit of frequency discrimination

Answer 38

The point below which two pure tones with slightly different frequencies are perceived as ONE single tone with a quality of “roughness”

Question 39

The critical band frequency

Answer 39

The point below which two pure tones with slightly different frequencies are percieved as TWO separate tones with a quality of “roughness”

Above the critical band, we hear two clear tones

Question 40

Roughness below critical band frequency

Answer 40

The two tones are exciting overlapping regions on the basilar membrane

Associated with dissonance