1. CALCULATING THE PROPERTIES OF WAVES
Essential question: Why do frequency and amplitude affect the amount of energy carried by the wave?

2. Simple harmonic motion: repetitive motion such as back-and-forth, up-and-down, or in a repeating circular motion.
Objects with simple harmonic motion (like waves) move with a defined period and defined frequency. Waves have simple harmonic motion.

3. “How much time to form one wave”
Frequency (f): The number of cycles (waves, oscillations, or vibrations) generated per second. Number of waves passing a reference point per second.
“How many per second”
Period (T): The time for one single vibration, oscillation, or wave. The time to generate one wave, or the time interval between successive waves.
“How much time to form one wave”
Frequency and period are inversely proportional to each other
As frequency increases, period decreases
As frequency decreases, period increases

4. High frequency wave—many waves per second
High frequency wave—many waves per second. Note that the period (time between sequential waves) is short.
Low frequency wave—fewer waves per second. Note that the period (time between sequential waves) is longer.

5. Calculating frequency (f) and period (T)
T = Period (seconds)
f = frequency (Hz)
t = time (seconds)

6. Wavelength (λ): The length of one wave
Wavelength (λ): The length of one wave. The distance between two identical positions on two consecutive (side-by-side) waves.
Wave speed (c): How fast waves move through a medium. The distance traveled by a wave per second.

7. Wave speed (m/s) Wave speed (m/s) d = distance (m) f = frequency (Hz)
(How far and the time)
Wave speed (m/s)
(Product of frequency and wavelength)
Wave speed (m/s)
d = distance (m)
f = frequency (Hz)
c = wave speed (m/s)
λ = wavelength (m)
t = time (s)
Wavelength (m)

8. Frequency and wavelength are inversely proportional to each other.
Higher frequency  Shorter wavelength
Lower frequency  Longer wavelength
Higher frequency
Lower frequency

9. Frequency and wavelength are inversely proportional to each other.
Higher frequency  Shorter wavelength
Lower frequency  Longer wavelength

10. Frequency and wave energy are proportional to each other.
Higher frequency (more waves)  more energy
Lower frequency (fewer waves)  less energy
Low frequency
Less energy
Higher frequency
More energy

11. Equilibrium position: Rest position
Equilibrium position: Rest position. The position of particles or spacing of particles in the medium when at rest. Equilibrium position is ½ way between the extremes of the wave.
Amplitude (A): The maximum displacement of particles in the medium from their equilibrium position as the wave passes through.
Amplitude is independent of all other wave properties except wave energy.
Amplitude is not affected by frequency or wave speed.

12. Low amplitude transverse wave
(crests & troughs are low)
High amplitude transverse wave
(crests & troughs are high)
Low amplitude longitudinal wave (condensations are less dense)
High amplitude longitudinal wave (condensations are more dense)

13. Amplitude is proportional to the energy of the wave because the wave displaces the medium as it moves through (performs work on the medium).
Higher amplitude  more work performed by wave.
Lower amplitude  less work performed by wave.

14. Damping: The gradual decrease in the wave amplitude that eventually will reach zero with time and propagation distance—loss of wave energy.
Waves spreading out over greater area—energy thins.
Gradual energy loss due to friction and heat to surroundings.

15. Solve for wave speed.
Sound waves travel through air. They move 1000 m in 3 seconds. Calculate the speed of sound.
Ripple waves on a pond’s surface travel 50 meters in 6 seconds. Calculate the wave speed.
A horn emits sound waves that have a frequency of 650 Hz and a wavelength of m. Calculate the speed of sound.

16. Solve the Problem
A guitar string vibrates at a rate of oscillations per minute. The speed of sound in air at 20ºC is 343 m/s.
Calculate the frequency (f) of the guitar string in Hz.
Calculate the period (T) of the vibration. (s)
Calculate the wavelength (λ) of the sound generated by the vibration. (m)

17. Solve the Problem
A horn emits a sound with a frequency of 6500 Hz. The speed of sound in air at 20ºC is 343 m/s.
Calculate the period (T) of the sound waves emitted from the horn. (s)
Calculate the wavelength (λ) of the sound waves. (m)

18. Waves on the ocean’s surface have a frequency of 2
Waves on the ocean’s surface have a frequency of 2.4 Hz and a wavelength of 5.9 meters.
Calculate the waves speed.
Calculate the period of the wave.
A horn produces a frequency of 780 Hz and a wavelength of meters.
Calculate the wave speed.
A horn produces a sound where the waves have a period of seconds and a wave speed of 350 m/s through air.
Calculate the frequency.
Calculate the wavelength.

19. Interpret the wave function
Interpret the wave function. Calculate the wavelength, frequency, period, and amplitude of the wave.
Wave speed (c) = 750 m/s

20. Interpret the wave function
Interpret the wave function. Calculate the wavelength, frequency, period, and amplitude of the wave.
Wave speed (c) = 1200 m/s