MCAT Physics and Math Review

Chapter 7: Waves and Sound

Conclusion

In this chapter, we reviewed the general characteristics of waves, including the phenomena of interference and resonance, and analyzed the characteristics and behaviors of sound as an example of a longitudinal waveform. Sound is the mechanical disturbance of particles creating oscillating regions of compression and rarefaction parallel to the direction of wave movement. The intensity of a sound wave is perceived as the sound level (loudness) of the sound and is measured in decibels. The decibel scale is a logarithmic scale used to describe the ratio of a sound’s intensity to a reference intensity (the threshold of human hearing). We also reviewed the Doppler effect and a special case with shock waves. We then reviewed the mathematics governing the formation of standing waves, which are important in the formation of musical sounds in strings, open pipes, and closed pipes. Finally, we discussed a medical application of sound that incorporates many of these topics: ultrasound.

Continue to review these MCAT topics—it’s easy to think about sound if you listen to music when you study! Whether you turn on Top 40, smooth jazz, or rococo fugues, the principles of sound production and propagation are key to your enjoyment of these harmonious sounds. Sound, of course, is not the only waveform tested on the MCAT. Light waves (and electromagnetic radiation in general) are heavily-tested topics on Test Day—we’ll review them in the next chapter.

Concept Summary

General Wave Characteristics

·        Transverse waves have oscillations of wave particles perpendicular to the direction of wave propagation (examples: “The Wave”, electromagnetic waves).

·        Longitudinal waves have oscillations of wave particles parallel to the direction of wave propagation (example: sound waves).

·        Displacement (x) in a wave refers to how far a point is from the equilibrium position, expressed as a vector quantity.

·        The amplitude (A) of a wave is the magnitude of its maximal displacement.

·        The maximum point of a wave (point of most positive displacement) is called a crest.

·        The minimum point of a wave (point of most negative displacement) is called a trough.

·        The wavelength (λ) of a wave is the distance between two crests or two troughs.

·        The frequency (f) of a wave is the number of cycles it makes per second. It is expressed in hertz (Hz).

·        The angular frequency (ω) is another way of expressing frequency and is expressed in radians per second.

·        The period (T) of a wave is the number of seconds it takes to complete a cycle. It is the inverse of frequency.

·        Interference describes the ways in which waves interact in space to form a resultant wave.

o   Constructive interference occurs when waves are exactly in phase with each other. The amplitude of the resultant wave is equal to the sum of the amplitudes of the two interfering waves.

o   Destructive interference occurs when waves are exactly out of phase with each other. The amplitude of the resultant wave is equal to the difference in amplitude between the two interfering waves.

o   Partially constructive and partially destructive interference occur when two waves are not quite perfectly in or out of phase with each other. The displacement of the resultant wave is equal to the sum of the displacements of the two interfering waves.

·        Traveling waves have continuously shifting points of maximum and minimum displacement.

·        Standing waves are produced by the constructive and destructive interference of two waves of the same frequency traveling in opposite directions in the same space.

o   Antinodes are points of maximum oscillation.

o   Nodes are points where there is no oscillation.

·        Resonance is the increase in amplitude that occurs when a periodic force is applied at the natural (resonant) frequency of an object.

·        Damping is a decrease in amplitude caused by an applied or nonconservative force.

Sound

·        Sound is produced by mechanical disturbance of a material that creates an oscillation of the molecules in the material.

·        Sound propagates through all forms of matter (but not a vacuum).

o   Sound propagates fastest through solids, followed by liquids, and is slowest through gases.

o   Within a medium, as density increases, the speed of sound decreases.

·        The pitch of a sound is related to its frequency.

·        The Doppler effect is a shift in the perceived frequency of a sound compared to the actual frequency of the emitted sound when the source of the sound and its detector are moving relative to one another.

o   The apparent frequency will be higher than the emitted frequency when the source and detector are moving toward each other.

o   The apparent frequency will be lower than the emitted frequency when the source and detector are moving away from each other.

o   The apparent frequency can be higher, lower, or equal to the emitted frequency when the two objects are moving in the same direction, depending on their relative speeds.

o   When the source is moving at or above the speed of sound, shock waves (sonic booms) can form.

·        Loudness or volume of sound (sound level) is related to its intensity.

o   Intensity is related to a wave’s amplitude.

o   Intensity decreases over distance and some energy is lost to attenuation (damping) from frictional forces.

·        Strings and open pipes (open at both ends) support standing waves, and the length of the string or pipe is equal to some multiple of half-wavelengths.

·        Closed pipes (closed at one end) also support standing waves, and the length of the pipe is equal to some odd multiple of quarter-wavelengths.

·        Sound is used medically in ultrasound machines for both imaging (diagnostic) and treatment (therapeutic) purposes.

Answers to Concept Checks

·        7.1

1.    Wave speed is the rate at which a wave transmits the energy or matter it is carrying. Wave speed is the product of frequency and wavelength. Frequency is a measure of how often a waveform passes a given point in space. It is measured in Hz. Angular frequency is the same as frequency, but is measured in radians per second. Period is the time necessary to complete a wave cycle. The equilibrium position is the point with zero displacement in an oscillating system. Amplitude is the maximal displacement of a wave from the equilibrium position. Traveling waves have nodes and antinodes that move with wave propagation. Standing waves have defined nodes and antinodes that do not move with wave propagation.

2.    If two waves are perfectly in phase, the amplitude of the resulting wave is equal to the sum of the amplitudes of the interfering waves. If two waves are perfectly out of phase, the amplitude of the resulting wave is the difference of the amplitudes of the interfering waves. Therefore, if the two waves are anywhere between these two extremes, the amplitude of the resulting wave will be somewhere between the sum and difference of the amplitudes of the interfering waves.

3.    False. Sound waves are the most common example of longitudinal waves on the MCAT.

4.    The object will resonate because the force frequency equals the natural (resonant) frequency. The amplitude of the oscillation will increase.

·        7.2

1.    Sound is produced by mechanical vibrations. These are usually generated by solid objects like bells or vocal cords, but occasionally can be generated by fluids. Sound is propagated as longitudinal waves in matter, so it cannot propagate in a vacuum.

2.    The amplitude of a wave is related to its sound level (volume). The frequency of a wave is related to its pitch.

3.    When two objects are traveling toward each other, the apparent frequency is higher than the original frequency  When two objects are traveling away from each other, the apparent frequency is lower than the original frequency  When one object follows the other, the apparent frequency could be higher, lower, or equal to the original frequency depending on the relative speeds of the detector and the source

4.    Ultrasound can be used for prenatal screening or to diagnose gallstones, breast and thyroid masses, and blood clots. It can be used for needle guidance in a biopsy, for dental cleaning, and for treating deep tissue injury, kidney stones, certain small tumors, cataracts, among many other applications.

5.   

Equations to Remember

(7.1) Wave speedν = 

(7.2) Period

(7.3) Angular frequency

(7.4) Speed of sound

(7.5) Doppler effect

(7.6) Intensity

(7.7) Sound level

(7.8) Change in sound level

(7.9) Wavelength of a standing wave (strings and open pipes)

(7.10) Frequency of a standing wave (strings and open pipes)

(7.11) Wavelength of a standing wave (closed pipes)

(7.12) Frequency of a standing wave (closed pipes)

Shared Concepts

·        Behavioral Sciences Chapter 2

o   Sensation and Perception

·        General Chemistry Chapter 8

o   The Gas Phase

·        Physics and Math Chapter 1

o   Kinematics and Dynamics

·        Physics and Math Chapter 2

o   Work and Energy

·        Physics and Math Chapter 8

o   Light and Optics

·        Physics and Math Chapter 10

o   Mathematics