Waves Review

Waves Review

• Pendulum Period (T)

  • Formula:
    ( T = 2\pi \sqrt{\frac{L}{g}} )

  • Rearranged:
    ( T^2 = 4\pi^2\frac{L}{g} )

  • Implications:

  • The period only depends on the length of the pendulum (L) and gravitational acceleration (g).

  • Longer length results in a longer period (T).

• Example Comparison of Periods:

  • Compare two pendulums, A and B both of length 10m:

  • Order of periods from least to greatest: A/B < C/D.

• Potential Energy (PE) in Springs:

  • Formula:
    ( PE = \frac{1}{2}kx^2 )

  • Doubling displacement (x) yields:

  • ( PE = \frac{1}{2}k(2x)^2 = 4 \cdot \frac{1}{2}kx^2 )

  • Result: PE quadruples with displacement doubling.

• K Constants and Spring Figures:

  • Example: k = 35 N/m, PE = ( \frac{1}{2}k(0.04)^2 )

  • For k=27 N/m, x=16cm,

  • Calculate PE using the formula above.

• Pendulum Energy Transition:

  • At the lowest point of the swing:

  • Kinetic Energy (KE) is maximum, Potential Energy (PE) is minimum.

  • At the highest points (ends of swing):

  • PE is maximum when KE is minimum.

• Spring Force Calculation:

  • Hooke's Law:
    ( F = -kx )

  • Example: For x = 0.12m, calculate the force.

• Wave Speed Calculation:

  • Formula:
    ( v = f\lambda )

  • Example: v = (6Hz)(6.0m) = 36m/s

  • Using wave velocity:

  • For f = 20Hz, d = 600m:
    v = fd = 12000m/s.

• Frequency and Wave Behavior:

  • Relationship between frequency and wavelength:

  • Lower frequency means higher wavelength.

  • Order of frequency from smallest to largest impacts wavelengths inversely.

• Constructive and Destructive Interference:

  • Constructive interference results in higher amplitude.

  • Always one more node than antinode in standing waves.

• Terminology:

  • Period, amplitude, wavelength, frequency are all related to wave behavior and characteristic definitions in physics.

• Understanding:

  • The maximum distance an object in simple harmonic motion moves from equilibrium: Amplitude, This value is crucial for understanding the energy carried by a wave, as greater amplitudes indicate more energy.

  • The shortest distance between two points where the wave pattern repeats: Wavelength,This measurement determines how closely spaced the wave cycles are, influencing both the frequency and speed of the wave.

  • The number of complete oscillations that a wave makes each second: frequency(Hz), is inversely related to the wavelength, meaning that higher frequencies correspond to shorter wavelengths, which affects how waves interact with their environment and propagate through different mediums.

  • The time needed for an object to complete one full cycle of simple harmonic motion is the: Period (T), which is a key factor in wave behavior as it determines the time taken for one complete wave cycle, thereby influencing both frequency and overall wave dynamics.

  • When more than one wave moves through the same medium at the same time, ______ occurs. Interference

  • Any motion that repeats in a regular cycle is called: periodic motion