Waves
What is a wave? A wave is a disturbance that transfers energy through a medium (the material that the wave travels through – air, water, a solid, etc). Two categories of waves: Mechanical (travel through matter) Electromagnetic (EM) (travel through space carrying radiant energy)
Some terms: When an object moves in a repeated patterns over regular time intervals, it is undergoing periodic motion. One complete repetition of the pattern is called a cycle, a vibration or an oscillation (N). The time required to undergo one cycle is called the Period (T).
Terms Rest or equilibrium position: the initial position of the object/medium. Ex. A pendulum hanging at rest Amplitude (A): the maximum displacement from rest position.
Two types of waves: Transverse wave: a wave in which the medium moves up and down, perpendicular to the direction of motion. Longitudinal wave: a wave in which the medium moves back and forth, parallel to the direction of motion.
Transverse Waves Crest (peak): high (maximum) point of a wave. Trough: low (minimum) point of a wave. Wavelength (λ): the distance between two crests, or two troughs. Ex. S waves of an earthquake, surface waves in the water, guitar string vibrating
Longitudinal Waves Compression: the region of the wave where the medium is compressed. Rarefaction: the region on the wave where the medium is expanded. Wavelength: measured from the center of one area of compression to the next (or one area of rarefaction to the next) Ex: sound waves, P waves of an earthquake, can be done with a slinky
Period and Frequency Period (T) is the time interval over the number of cycles that occur within that time interval. T = ∆t/N Where time is measured in s and N is just the number of cycles, no units. Thus, the unit for T is also s. Frequency (f) the number of cycles per time interval. f = N/∆t Units for frequency are Hz (“hertz”). 1 Hz = 1 /s This makes the frequency the inverse of the period (f = 1/T)
Examples: Ex1. A mass suspended from a spring vibrates up and down 24 times in 36 seconds. Find the period and frequency of the vibration. T = ∆t/N = 36s/24 = 1.5s f = N/∆t = 24/36 s = 0.67 Hz (or, f= 1/T = 1/1.5s = 0.67 Hz)
Ex2. Most butterflies beat their wings between 450. and 650 Ex2. Most butterflies beat their wings between 450. and 650. times per minute. Calculate the range of typical wing-beating frequency of butterflies. Lower range: f = N/∆t = 450/60s = 7.50 Hz Upper range: f = N/∆t = 650/60s = 10.8 Hz Range of frequency: 7.50-10.8 Hz
Waves and speed The speed with which a wave moves depends on the nature of the medium. The speed of a wave is the product of the wavelength of the lave and its frequency. v = fλ Where frequency is measured in Hz (/s) and wavelength is measured in m.
Examples Ex1. A student vibrates the end of a spring with a frequency of 2.8 Hz. This produces a wave with a wavelength of 0.36 m. What is the speed of this wave? v = fλ = 2.8Hz x 0.36m = 1.0 m/s
Ex2. Water waves with a wavelength of 2 Ex2. Water waves with a wavelength of 2.8m, produced in a wave tank, travel with a speed of 3.8 m/s. What is the frequency of the straight vibrator that produced these waves? If v = fλ, then f = v/λ = 3.8m/s / 2.8m = 1.4 Hz