Wave Properties Objective 1Describe wave motion in terms

Wave Properties Objective: 1)Describe wave motion in terms of wavelength, frequency, amplitude, and energy. 2) Identify various types of waves. 3) Explain wave properties and resulting phenomena.

Bellwork 04/19/2011 A person on a pier observes a set of incoming waves that have a sinusoidal form with a distance of 1. 6 m between the crests. A wave laps against the pier every 4. 0 s. A) What is the frequency of the waves? B) What is the speed of the waves?

Bellwork Solution • Given: =1. 6 m and T = 4. 0 s • A) f=1/T =(4. 0 s)-1 = 0. 25 s-1 = 0. 25 Hz • B) v = f = (1. 6 m)(0. 25 Hz) = 0. 40 m/s

Baseball Partners • Please take out a piece of paper and sketch a baseball diamond on it. • Find a different partner who does not sit at your table for each of the three bases and for homeplate. • Write the partner’s name at each location.

Longitudinal Waves • A longitudinal wave is a wave in which particles of the medium (the propagation of the wave) move in a direction parallel to the direction which the wave moves (the velocity of the wave).

Transverse Waves • A transverse wave is a wave in which the particles of the medium are displaced in a direction perpendicular to the direction of energy transport.

Surface Waves – Elliptical and Torsional • A surface wave is a wave in which particles of the medium undergo a circular or elliptical motion.

Example 1 • Olive Udadi accompanies her father to the park for an afternoon of fun. While there, she hops on the swing and begins a motion characterized by a complete back -and-forth cycle every 2 seconds. What is frequency of her swing?

Example 1 Solution Olive Udadi accompanies her father to the park for an afternoon of fun. While there, she hops on the swing and begins a motion characterized by a complete back-and-forth cycle every 2 seconds. What is frequency of swing is? • Frequency refers to the number of occurrences of a periodic event per time and is measured in cycles/second. In this case, there is 1 cycle per 2 seconds. So the frequency is 1 cycles/2 s = 0. 5 Hz.

Waves Transport Energy • The energy transported by a wave is directly proportional to the square of the amplitude of the wave. E = k. A 2

Example 2: Mac and Tosh stand 8 meters apart and demonstrate the motion of a transverse wave on a slinky. The wave can be described as having a vertical distance of 32 cm from a trough to a crest, a frequency of 2. 4 Hz, and a horizontal distance of 48 cm from a crest to the nearest trough. Determine the amplitude, period, and wavelength of such a wave.

Solution to Example 2 • Amplitude = 16 cm Amplitude is the distance from the rest position to the crest position which is half the vertical distance from a trough to a crest. • Wavelength = 96 cm Wavelength is the distance from crest to crest, which is twice the horizontal distance from crest to nearest trough. • Period = 0. 42 s The period is the reciprocal of the frequency. T=1/f

Warm-Up A spider swings in the breeze from a silk thread with a period of 0. 6 s. How long is the spider’s strand of silk?

The Speed of a Wave • If the crest of an ocean wave moves a distance of 20 meters in 10 seconds, then the speed of the ocean wave is 2 m/s. • If the crest of an ocean wave moves a distance of 25 meters in 10 seconds (the same amount of time), then the speed of this ocean wave is 2. 5 m/s. • The faster wave travels a greater distance in the same amount of time.

Example 3 • The time required for the sound waves (v = 340 m/s) to travel from the tuning fork to point A is ____.

Solution to Example 3 GIVEN: v = 340 m/s, d = 20 m and f = 512 Hz Use v = d / t and rearrange to t = d / v Substitute and solve. t = d/v = 20 m/340 m/s = 0. 059 s

Variables Affecting Wave Speed

Speed of a Wave Lab - Sample Data Trial Tension Frequency Wavelength Speed (N) (Hz) (m/s) 1 2 3 4 5 6 7 8 2. 0 2. 0 5. 0 4. 05 8. 03 12. 30 16. 2 20. 2 12. 8 19. 3 25. 5 4. 00 2. 00 1. 33 1. 00 0. 800 2. 00 1. 33 1. 00 16. 2 16. 1 16. 4 16. 2 25. 6 25. 7 25. 5

Wave speed is dependent upon medium properties and independent of wave properties. • the wave speed is calculated by multiplying wavelength by frequency, an alteration in wavelength does not affect wave speed. • alteration in wavelength affects the frequency in an inverse manner yet the wave speed is not changed.

Tension and Wave Speed • Natural frequencies depend on mass, linear mass density, tension force, internal structure, and other conditions • For a stretched string where FT is the tension on the spring and μ is the linear mass density (m/L) for n = 1 (the first harmonic)

Example 4: Tuning a Guitar String A. Suppose you want to increase the fundamental frequency of a guitar string. Would you have to tighten it or loosen it? B. To change from the A note (220 Hz) below middle C to the A note above middle C (440 Hz) using steel guitar strings (density=7. 8 x 103 kg/m) and the initial thicker string has a diameter of 0. 30 cm, could you replace it with a thinner string with half the diameter?

Solution to Example 4 A. Tightening the string causes a higher frequency B. Yes: f 1= 220 Hz, f 2= 440 Hz Assuming L is constant for both strings (distance between bridge and neck), μ depends only on the diameter of the string because mass depends on density and volume… m = D*V and V = r 2 L; thus m = D* r 2 L μ = m/L = D* r 2 L/L So how is frequency related to diameter? f 1/d

Superposition of Waves • When two or more waves travel through the same medium at the same time, they interfere in a process called superposition. • At any time, the combined waveform of two or more interfering waves is given by the sum of the displacements of the individual waves at each point in the medium.

Interference • Constructive Interference: The vertical displacements of the two pulses are in the same direction and the amplitude of the combined waveform is greater than that of either pulse.

Interference • Destructive Interference: The amplitude of the combined waveform is smaller than that of either pulse.

Applications of Destructive Interference • Automobile mufflers • Active noise cancellation headphones • Fourier-transform Infrared Spectrometry – identify unknown materials – determine the quality or consistency of a sample – determine the amount of components in a mixture

Boundary Behavior • Reflection: a wave strikes an object or comes to a boundary with another medium and is diverted back into the original medium (echo of sound) • Refraction: a wave crosses a boundary with another medium and its speed changes (spear fishing) • Dispersion: Waves of different frequencies spread apart from one another (light through a prism) • Diffraction: bending of waves around the edge of an object (polarization)

Fixed End Reflection for Standing Waves Describe the motion of the incident pulse compared to the reflected pulse.

Free End Reflection for Standing Waves • Describe the motion of the incident pulse compared to the reflected pulse.

Independent Practice • p. 463 -465; 66, 67, 79, 81, 85, 88, 93, 100 • Wave on a String Activity • Explore Online http: //phet. colorado. edu/index. php – Waves on a String Simulation – Ripple Tank Simulation