Unit 6 review 23-24

Unit 6 Review Notes

Measuring Wavelength and Amplitude

Wavelength:

• The wavelength of a wave is the distance between two consecutive crests (or troughs) of the wave. In our measurements, it was found to be 1.3 cm, which indicates the spatial period of the wave. Longer wavelengths can carry lower frequency signals, while shorter wavelengths carry higher frequency signals.

Amplitude:

• Amplitude is defined as the maximum displacement of points on a wave from its equilibrium position. It was measured from the equilibrium line to either the crest (the highest point) or trough (the lowest point) of the wave, resulting in an amplitude of 1.4 cm. This measurement is crucial as it determines the energy level of the wave; greater amplitudes correspond to higher energies.

Understanding Period and Frequency

Definitions:

• Frequency (f): Refers to the number of cycles (complete waveforms) that occur in one second and is expressed in Hertz (Hz). For example, a frequency of 2 Hz means that two cycles occur every second.

• Period (T): This is the duration taken for one complete cycle of the wave to pass a given point, measured in seconds.

Relationships and Inverses:

• The period and frequency are inversely related and can be expressed with the formula: T = 1/f. This means as frequency increases, the period decreases proportionately.

• Wave Speed (v) is related to wavelength (λ) and frequency (f) through the equation: v = λf. This shows that the speed of a wave is the product of its wavelength and frequency. Therefore, if one increases, the other must adjust to maintain constant speed unless the characteristics of the medium change.

Example Calculation:

• Given a frequency of 60 Hz, the period can be calculated as:

  • T = 1/60 = 0.0167 seconds.

• If the speed of the wave is 30 m/s, the wavelength can be calculated using the relationship: Wavelength (λ) = Speed (v) / Frequency (f):

  • λ = 30 m/s / 60 Hz = 0.5 m.

Finding Speed from Wavelength and Period

Example:

• If one wave occurs every 12 seconds, we can determine:

  • Period (T) = 12 seconds.

  • Frequency (f) = 1/12 Hz = 0.0833 Hz.

• For a known wavelength of 200 m, the speed can be calculated as:

  • Speed (v) = Wavelength / Period = 200 m / 12 s = 16.7 m/s.

Seismic Waves: P-waves and S-waves

P-waves:

• These are primary waves, or compressional waves, that travel faster than S-waves and can move through solids and liquids. For example, if the speed is given as 500 km/s (which converts to 5000 m/s), and with a wavelength of 150 m, the frequency is calculated as follows:

  • Frequency (f) = Speed (v) / Wavelength (λ) = 5000 m/s / 150 m = 33.3 Hz.

  • It's essential to ensure consistent unit conversions throughout calculations to avoid errors.

S-waves:

• Secondary waves, or shear waves, which are slower than P-waves and can only travel through solids. If the S-wave speed is given as 2.8 km/s (convert to 2800 m/s), using the same frequency of 33.3 Hz, we arrive at:

  • Wavelength (λ) = Speed / Frequency = 2800 m/s / 33.3 Hz = 84 m.

Arrival Times of Seismic Waves

• For an example where the P-wave travels a distance of 200 km at a speed of 5 km/s, the time is calculated as:

  • P-wave Arrival Time = 200 km / 5 km/s = 400 seconds.

• For the S-wave, with a slower speed, it results in:

  • S-wave Arrival Time = 200 km / (2.8 km/s) = 714 seconds.

• This leads to an SP interval, or difference in arrival times, calculated as:

  • SP Interval = 714 s - 400 s = 314 seconds.

Wave Interference

• When two transverse waves meet, they combine through constructive or destructive interference, leading to a resultant wave.

Constructive Interference:

• This occurs when two waves meet in-phase, meaning their crests and troughs align. The amplitudes of the overlapping waves add together, resulting in a new wave of greater amplitude. For example, if a small amplitude wave of 1 unit meets a larger wave of 2 units, the resultant wave would have an amplitude of 3 units.

Destructive Interference:

• This occurs when two waves meet out of phase, meaning the crest of one wave aligns with the trough of another. In this case, the amplitudes subtract from each other, which may result in a wave of smaller amplitude or even complete cancellation. For instance, if a wave with an amplitude of 2 units meets another wave of -2 units (trough), they would completely cancel each other out, resulting in no wave.

Standing Waves on a String

Nodes and Antinodes:

• In a standing wave formed on a string, nodes are points of no displacement (where the string does not move), located at each end of the string, while antinodes represent points of maximum displacement, typically found at the middle.

Wavelength Calculation:

• For a fundamental frequency established across a string of length 1 m, one can observe that the arrangement produces one full wave across the length, meaning:

  • Wavelength (λ) = 2 m (as one wavelength encompasses two nodes).

Frequency calculation based on harmonic series:

• 1st Harmonic: 25 Hz (λ = 2m)

• 2nd Harmonic: 50 Hz (λ = 1m)

• 3rd Harmonic: 75 Hz (λ = 0.67m)

• 4th Harmonic: 100 Hz (λ = 0.5m)

Types of Plate Boundaries

Transform Boundaries:

• These boundaries are characterized by tectonic plates sliding past each other in a side-by-side motion, which can generate earthquakes with magnitudes up to 8.0, primarily shallow in depth. They experience little volcanic activity and are found in regions like the San Andreas Fault in California.

Divergent Boundaries:

• At these boundaries, tectonic plates separate, leading to the formation of rift zones and significant underwater features such as mid-ocean ridges. The geological activity is marked by volcanic activity, often involving low-magnitude, continuous eruptions as new crust forms.

Convergent Boundaries:

• These boundaries occur where plates collide, which can involve oceanic with continental plates, or oceanic plates converging with each other, leading to subduction zones. Earthquakes magnitudes can erupt up to 9.5, with a prevalence of deep focus earthquakes, creating volcanic arcs such as those found in the Andes Mountains. Notably, earthquakes also frequently occur inland where plates undergo compression.

Key Concepts of Earthquake Hazards

• Tsunamis: Major seismic waves commonly associated with convergent boundaries or subduction zones, posing significant risk to coastal regions.

• Recycling Old Crust: At convergent boundaries, denser oceanic plates subduct beneath lighter continental plates, impacting crustal dynamics.

• Mountain Building: The collision of continental plates can create uplift, leading to high mountain ranges like the Himalayas, demonstrating the dynamic nature of Earth's geological processes.

Final Notes

• It's imperative to review SP intervals as recorded in seismograms to better understand wave arrival times and characteristics. Consistent clarity regarding wave mechanics and thorough attention to unit conversions during calculations are vital for educational accuracy and understanding.