Sound

Question 1

Which type of wave is a sound wave?

Answer 1

Sound waves are longitudinal.

Longitudinal waves oscillate in the direction of the propagation of the wave. Note that sound waves are different from light waves, which are transverse. Transverse waves oscillate perpendicularly to the medium.

Question 2

Describe the effect that a propagating sound wave has on the particles within the medium.

Answer 2

1. Starting at an initiation point, particles pulse outward towards their neighbors, creating a high-density region.
2. The high-density wavefront continues outward, while the original particles settle back into the now much lower-density region that they initially occupied.
3. This high-then-low density pulse is a sound wave, and can exist in any medium.

Question 3

What two properties of a medium most directly affect the speed of sound?

Answer 3

elasticity and density

Recall that sound wave propagation involves both the compression and the rarefaction (spreading out) of a medium. Mediums that can bounce back faster and have less mass per volume will allow sound to travel at a greater rate. On the MCAT, “bulk modulus” is often mentioned instead of elasticity, but the principle is the same.

Question 4

Through which metal should sound travel faster: nickel or bronze?

Assume that both substances have relatively equal density, but nickel has a greater bulk modulus.

Answer 4

It travels faster in nickel.

The speed of sound in a material is directly proportional to the material’s bulk modulus. In other words, since nickel has a higher modulus, it is more elastic (its particles bounce back more readily after displacement). This allows for faster sound wave propagation.

Question 5

Through which substance should sound travel faster: protium (¹₁H) or deuterium (²₁H)

Assume that both substances have roughly the same number of particles per unit volume.

Answer 5

It travels faster in protium.

Since deuterium has twice the mass of protium, it will have twice the density as well. Assuming that the bulk moduli are similar, the substance with the smaller density allows for faster sound wave propagation.

Question 6

Rank the phases of matter, from the phase which sound travels through fastest to that which it travels through slowest.

Answer 6

Sound will travel fastest in solids, followed by liquids. Finally, sound travels through gases the most slowly. Note that sound does not propagate at all in a vacuum.

The speed of sound is about 5120 m/s in iron, 1480 m/s in water, and 330 m/s in air.

Question 7

What is the speed of sound in air at STP?

Answer 7

It is around 330 m/s at STP.

The expression c is generally used for the textbook speed of light, but can be used for sound as well. The constant speed of sound of air, then, could be denoted simply as c.

Question 8

What quantity is generally measured in decibels?

Answer 8

intensity

Intensity is generally given in units of W/m². The decibel convention is a logarithmic scale that makes these numbers more manageable.

Question 9

Define:

intensity

Answer 9

Intensity (here, in reference to sound) is the power per unit area of the wave.

The standard reference value for intensity is 10^-12 W/m².

Question 10

What kind of relationship exists between the intensity of sound and the decibel scale?

Answer 10

A logarithmic relationship exists between decibels (L), intensity (I’), and baseline intensity (I₀), such that:

dB = 10*log(I’ / I₀)

Technically, a decibel value is a dimensionless quantity since it describes a ratio between the baseline value and the observed value.

Question 11

What shortcut can be used to calculate log(Z) when Z = n x 10^e?

Answer 11

If Z = n x 10^e, then log(Z) approximately equals e.n.

For example, if Z = 6.2 x 10⁴, then n = 6.2 and e = 4. Log(Z) can then be approximated as equal to

(4).(6.2) = 4.62

Note that the real value of log(Z) = 4.79. On the MCAT, approximate answers are virtually always acceptable, and rounding is generally a useful and time-saving strategy.

Question 12

What decibel value corresponds to an intensity reading of 10^-10 W/m²?

Answer 12

20 dB

dB = 10*log(I’ / I₀) = 10*log(10^-10 / 10^-12)
10*log(10²) = 10*2 = 20 dB

With regard to intensity, 20 dB is on the lower end of the human hearing scale; it corresponds to a low whisper. Note that 10^-12, which represents the quietest sound that can be detected by a typical human ear, is a commonly-used reference intensity.

Question 13

What decibel value corresponds to an intensity reading of 10² W/m²?

Answer 13

140 dB

dB = 10*log(I’ / I₀) = 10*log(10² / 10^-12)
10*log(10¹⁴) = 10*14 = 140dB

140 dB is around the highest intensity of sound that humans can hear without going deaf. It corresponds to the intensity heard when very close to a jet engine during take-off.

Question 14

What is the difference in intensity between a shout (50 dB) and a loud stereo (80dB)?

Answer 14

The stereo is 1000 times the intensity of the shout.

Recall that the dB scale is logarithmic, so that every increase of 10dB corresponds to an intensity increase of a factor of 10. A 30 dB increase must then be a 10³-fold increase in intensity.

Question 15

Define:

attenuation

This term has multiple meanings; here, define it as it relates to sound.

Answer 15

It is the gradual drop in intensity of sound as it passes through a medium.

This generally occurs due to the absorption of wave energy by the medium. As intensity decreases, the amplitude of the wave will become lower as well.

Question 16

Define:

pitch

Answer 16

It is the frequency of a sound, generally referenced in the form of a comparison. For example, a certain sound may be “higher-pitched” while another is “lower-pitched.”

Often, one pitch is set as a standard to gauge others against. The pitch “A above middle C” is often used as such a reference and is paired with a frequency of 440Hz.

Question 17

Two off-pitch A notes have slightly different frequencies. If one has a frequency of 446 Hz while the other is measured at 465 Hz, which sound is higher-pitched?

Answer 17

465-Hz

Pitch is generally given as a comparison between tones, where the higher-frequency tone is higher in pitch. Here, 465 Hz is high compared to 446 Hz.

Question 18

What is the relationship between wave speed, wavelength and frequency?

Answer 18

v_c = f λ

This is the most important wave relationship to know for the MCAT.

Question 19

If the frequency of a sound wave in air doubles, how does its wavelength change?

Answer 19

Its wavelength will decrease to 1/2 of its previous value.

v_c = f λ

Frequency and wavelength are inversely proportional, since the speed of sound in air is constant. As frequency doubles, wavelength must be halved.

Question 20

If a sound wave enters a new medium that causes its speed to be halved, how does its wavelength change?

Answer 20

Its wavelength will decrease to 1/2 of its previous value.

v_c = f λ

When a sound wave moves from one medium to another, its frequency will not change. Speed and wavelength, then, must be directly proportional. As the speed is reduced by half, the wavelength must be halved as well.

Question 21

When a fire truck is traveling towards an observer, its siren sounds higher-pitched than when it is moving away. What name is given to this phenomenon?

Answer 21

This situation is an example of the Doppler effect.

The Doppler effect describes the change in observed frequency of a wave, compared to the frequency that is actually emitted. For a shift in frequency to take place, the source and the observer of the sound must be moving in relation to each other.

Question 22

What formula can be used to calculate the Doppler shift in frequency?

Answer 22

f’ = f_o (v_c ± v_d) / (v_c ± v_s)

Where:

f_o = emitted frequency (Hz)
f’ = perceived frequency (Hz)
v_c = speed of sound (m/s)
v_d = speed of observer (m/s)
v_s = speed of source (m/s)

While virtually all MCAT questions can be answered without exact use of this formula, it is important to know what factors will cause perceived frequency to be higher or lower than emitted frequency.

Question 23

A motorcycle emits a sound as it moves at 20 m/s. A motorist, traveling at 20 m/s in the same direction, hears the sound. What will be the Doppler shift from the emitted frequency?

Answer 23

The motorist will hear no difference; in other words, perceived frequency and emitted frequency will be the same.

For a Doppler shift to take place, the source and observer must be in motion relative to each other. If both are moving in the same direction and at the same speed, no relative motion exists.

Question 24

A motorcycle emits a sound as it travels at 20 m/s toward a stationary observer. How will the observed frequency differ from the emitted frequency?

Answer 24

The observed frequency will be higher than the emitted frequency.

When the source and the observer are moving toward one another, perceived frequency will increase. This happens regardless of whether the source alone, the observer alone, or both entities are moving.

Question 25

A parked ice cream truck emits a sound that is heard by an observer driving toward it at 20 m/s. How will the observed frequency differ from the emitted frequency?

Answer 25

The observed frequency will be higher than the emitted frequency.

When the source and the observer are moving toward one another, perceived frequency will increase. This happens regardless of whether the source alone, the observer alone, or both entities are moving.

Question 26

A fire truck emits a siren as it travels west. The siren is heard by an eastward-traveling bicyclist located east of the fire truck. How will the observed frequency of the siren differ from its emitted frequency?

Answer 26

The observed frequency will be lower than the emitted frequency.

When the source and the observer are moving away from one another, perceived frequency will decrease. This happens regardless of whether the source alone, the observer alone, or both entities are moving.

Question 27

What information is given by the frequency of a wave?

Answer 27

A wave’s frequency is the number of cycles, or total waves, that cross a certain point within a certain timespan.

Frequency is generally measured in hertz (Hz). The units for hertz are 1/s, which can be thought of as cycles or revolutions per second.

Question 28

What term is given to the distance between adjacent peaks (or the distance between adjacent troughs) on a waveform?

Answer 28

wavelength

The wavelength is the distance from a starting position to the same position on the adjacent wave. When wave speed is constant, wavelength is inversely proportional to frequency.

Question 29

Imagine a sine wave. What term is given to the vertical distance between the equilibrium position of the waveform (the x-axis) and its peak?

Answer 29

amplitude

A wave’s amplitude is the displacement between its equilibrium position and a peak or trough. Amplitude directly relates to the intensity, or loudness, of the sound.

Question 30

With regard to sound waves, what term is given to the part of the diagram shown by the arrow?

Answer 30

node

In a standing wave, nodes are the parts of the wave that remain fixed in position.

Question 31

With regard to sound waves, what term is given to the part of the diagram shown by the arrow?

Answer 31

antinode

In a standing wave, antinodes are the parts of the wave that undergo the largest displacements.

Question 32

What features must characterize a standing wave in an open pipe?

Answer 32

The term open pipe is used to signify that both ends are open, not just one. The ends must have antinodes at both positions and at least one node between them.

The wave above depicts the 4th harmonic, since it has 4 nodes.

Question 33

What features must characterize a standing wave in an closed pipe?

Answer 33

The term closed pipe is used to signify that one end is open and one is closed. The open end must contain an antinode, while the closed end must display a node.

A common misconception is that both ends are closed; do not fall for this trap. All types of pipes must have at least one open end.

Question 34

Describe the specific standing wave that can exist on a string with both ends fixed in place.

Answer 34

A string with both ends fixed must have nodes at both ends and at least one antinode between them.

The wave depicted above is the 3rd harmonic, since it has 3 antinodes.

Question 35

How is the harmonic number determined for different types of standing waves?

Answer 35

For any standing wave with at least one end open, count the total number of nodes contained in a single wavelength.

For a standing wave with both ends fixed, count the total number of antinodes contained in a single wavelength.

Question 36

To mathematically describe a standing wave, what information is needed apart from the shape and type of medium?

Answer 36

The harmonic number is required to fully understand the wave.

Given the shape of the wave (closed or open), type of medium (air, water, etc.), and the harmonic number, all other values can be calculated.

Question 37

How many nodes and antinodes will be present in the fourth harmonic of a wind chime pipe with both ends open?

Answer 37

Since this is the fourth harmonic, four nodes must exist between the two ends. Five antinodes are also present: one at each end and three between the nodes.

Question 38

How many nodes and antinodes will be present in the third harmonic of a guitar string that has both ends fixed in place?

Answer 38

Since this is the third harmonic, three antinodes must exist between the two ends. Four nodes are also present: one at each end and two between the antinodes.

Question 39

Define:

ultrasound

Answer 39

It is the region of sound just above the range of human perception.

Specifically, this is the region around 20,000 Hz and higher. Medical applications use sound at the level of megahertz and gigahertz.

Question 40

If a bat can hear sounds up to 22,000 Hz, how does that change the range of ultrasound?

Answer 40

The range of ultrasound does not change.

Ultrasound is relative to human hearing. Regardless of other factors, it refers to the range of sound above 20,000 Hz.