Week 2- Wave Characteristics

objectives Recap wave basics. Understand and define few more wave characteristics Wavelength, amplitude, frequency, period, velocity

Quick recap of wave basics A wave is a disturbance that transfers energy. Wave classification Mechanical waves, Electromagnetic waves. Another way, Transverse, Longitudinal, Surface, Torsional waves. Wave characteristics we discussed earlier. Crest, Trough, Amplitude, Wavelength.

CHARACTERISTICS OF WAVES Waves are described according to their Amplitude measures DISPLACEMENT size of the disturbance Wavelength  distance of a “repeating unit” Also called a cycle Velocity v speed = how fast wave travels

AMPLITUDE A Distance between “rest & crest” or “rest & trough” Gives indication of “power” or “strength” of wave (magnitude of earthquake = Richter scale) Does not affect velocity of wave Determines loudness (sound) or brightness (EM wave)

Frequency ƒ How often? Number of wavelengths that pass any point per unit of time. measured in wavelengths/second or cycles/second Hertz (Hz*) = number of wavelengths in 1 second *  Heinrich Rudolf Hertz, a 19th century physicist 

PERIOD T Period = 1 Frequency = 1 How long? Amount of time for one wavelength to pass a point Related inversely to frequency Period = 1 Frequency Frequency = 1 Period When an event occurs repeatedly, then we say that the event is periodic and refer to the time for the event to repeat itself as the period. Note: Inverse relationship

Period and Frequency Watch: World’s fastest everything If Tim clapped 780 times in one minute, what’s the frequency? If Jane stamped 100 checks in 40 seconds, what’s the frequency?  A pendulum is observed to complete 23 full cycles in 58 seconds. Determine the period and the frequency of the pendulum

WAVELENGTH  Distance between any two repeating points on a wave crest-crest, trough-trough, expansion-expansion, compression- compression Determines what colors we see; what notes we hear (pitch) Shorter wavelengths have more cycles per minute because they aren’t as long

VELOCITY v the rate at which the energy travels; speed & direction Depends on medium Mechanical waves travel faster through dense mediums EM Waves are faster through less dense mediums

Calculating Wave Speed Speed = wavelength x frequency V = λ x f V = velocity (m/s) λ = wavelength (m) f = frequency (Hz; 1/sec)

Examples What is the speed of a wave with a wavelength of 2m and a frequency of 3 Hz? V = λ x f V = (2)(3) V = 6 m/s A wave is traveling at a speed of 12 m/s and its wavelength is 3m. Calculate the wave’s frequency. 12 = (3)(f) 12 = f 3 4 Hz = f

Homework Watch it one more time: https://www.youtube.com/watch?v=gi7SeYefIVI Understand and memorize equations relating, 1) Frequency and Period 2) Velocity and Wavelength. Solve the problem sheet provided in the class. In case you lost this. You can print here: See next slide for extra credit!

Extra credit Solve the following and send me the response via email before our next meeting: Problem 1: Jerome and Claire are doing the Period of a Pendulum Lab. They observe that a pendulum makes exactly 10 complete back and forth cycles of motion in 21.8 seconds. Determine the period of the pendulum. Problem 2: Strong winds can apply a significant enough force to tall skyscrapers to set them into a back-and-forth motion. The amplitudes of these motions are greater at the higher floors and barely observable for the lower floors. It is said that one can even observe the vibrational motion of the Sears Tower in Chicago on a windy day. As the Sears Tower vibrates back and forth, it makes about 8.6 vibrations in 60 seconds. Determine the frequency and the period of vibration of the Sears Tower. Problem 3: The spin rate of a CD-ROM varies according to the location on the disc from where data is being accessed. When accessing data from the inner circles of the disc, the CD can spin at a rate as high as 400 revolutions per minute. Determine the frequency (in Hertz) and the period (in seconds) of the spinning CD. Problem 4:Like all planets, the planet Venus orbits the Sun in periodic motion and simultaneously spins about its axis. Just as on Earth, the time to make one complete orbit (i.e., the period of orbit) is what defines a year. And the time to make one complete revolution about its axis (i.e., the period of rotation) is what defines a day. The period of orbit for the Earth is 365.25 days and the period of rotation is 24 hours (1.00 day). But when these same values for Venus are expressed relative to Earth, it is found that Venus has a period of orbit of 225 days and a period of rotation of 243 days. So for Venus inhabitants, a day would last longer than a year! Determine the frequency of orbit and the frequency of rotation (in Hertz) on Venus. Problem 5: Extreme waves along ocean waters, sometimes referred to as freak waves or rogue waves, are a focus of much research and study among scientists. Several merchant ships reports rogue waves which are estimated to be 25 meters high and 26 meters long. Assuming that these waves travel at speeds of 6.5 m/s, determine the frequency and the period of these waves.