Waves A wave is a that propagates p in a certain direction with a certain speed. 1D 2D 3D Physical medium Waves in water Waves in elastic bodies Sound Empty space (a vacuum) Electromagnetic waves HITES, 2011 Lecture 1 1 Waves: Basic definitions You are in a boat out on the ocean watching the waves go by. To fully describe the waves, you need three things: 1. A 2. λ 3. f Units of frequency: Hz = waves/second T, period. Time for one wavelength to pass. T=1/f v, wave velocity. How fast the wave is moving. v= λf HITES, 2011 Lecture 1 2
Examples: Tsunami and Ultrasound Satellite photos of the December 26, 2004 tsunami showed a spacing of wave crests of 800 km and a period between the waves of 1 hour. Find the speed of the waves in km/hr. In a typical ultrasound, waves travel through body tissue with a speed of 1500 m/s. For a good detailed image, the wavelength should be no more than 1 mm. Find the frequency required for a good scan. HITES, 2011 Lecture 1 3 Example: Fishing Dr. Bennett is out fishing. Since the fish are not biting, he starts counting waves. He counts 41 wave crests in 1.3 minutes and he estimates the distance between the crests to be 2.7 m. What is the wavelength (m)? What is the frequency (Hz)? What is the wave speed (m/s)? HITES, 2011 Lecture 1 4
Some Types of Waves Transverse Longitudinal HITES, 2011 Lecture 1 5 Animation courtesy of Dr. Dan Russell, Kettering University HITES, 2011 Lecture 1 6
Power and Energy in Waves Waves transfer energy, without the transfer of mass. Power is energy per time. Power transmitted in a wave is proportional to: square of the frequency square of the amplitude Ocean Waves: Quite complex; 3 m high wave, 8 sec period Power generated is 70.6 kw/m At 20% efficiency, 0.08 m crest length needed per house HITES, 2011 Lecture 1 7 Wave Intensity Average power transferred across unit area perpendicular to energy flow. I P Surface Area P 4 r 2 2 1 I 2 r I 1 2 2 r I 1 r 2 HITES, 2011 Lecture 1 8
Example: Tornado Warning Siren A tornado warning siren can produce a sound of intensity 0.25 W/m 2 at 15 m away. What is the intensity at 30 m away? To hear the siren, it should have a greater intensity than normal conversation, which is 1x10-6 W/m 2. How far away can you hear the siren? HITES, 2011 Lecture 1 9 Interference : waves add together th Obstacle : echo remains the same Wave reflection HITES, 2011 Lecture 1 11
Example: Rope A cord has two sections as shown in the figure. An incident wave travels along section 1 with wavelength λ 1 = 2.95 m and frequency f = 2.83 Hz. The transmitted wave has wavelength λ 2 =149m 1.49 m. What is the wave speed (m/s) in section 1? What is the wave speed (m/s) in section 2? HITES, 2011 Lecture 1 12 Waves: Interference : displacements in same direction : displacements in opposite direction Interference in Two Dimensions Superposition of Waves HITES, 2011 Lecture 1 13
Standing Waves Results from superposition of two or more waves traveling in opposite directions. Certain periodic excitation produces patterns of motion so the wave appears to be stationary or standing. Wave appears to NOT travel up and down the string. HITES, 2011 Lecture 1 14 Standing Waves Frequencies of standing waves are the, or resonant frequencies. Lowest natural frequency is the natural frequency, or the first. Higher frequencies are called harmonics, or sometimes Second frequency is first overtone Can have standing waves in other objects, e.g. drum heads, metal (bells), and air columns (organ pipes). HITES, 2011 Lecture 1 15
Example: French Horn The French horn produces tones composed almost entirely of the fundamental and second harmonic. Draw the superimposed wave. HITES, 2011 Lecture 1 16 Effect of Overtones on Sound The contribution of overtones will change how we hear the sound Examine the same frequency with different contributions ti of overtone http://www.falstad.com/fourier/index.html HITES, 2011 Lecture 1 18
Electromagnetic Waves Phenomenon that takes the form of selfpropagating waves in a vacuum or in matter. Examples of electromagnetic radiation HITES, 2011 Lecture 1 19 Electromagnetic Spectrum Speed of electromagnetic waves: 3.00x10 8 m/s (speed of light) Frequencies: detected from 1 to 10 24 Hz Wavelengths: 10-16 to 10 8 meters HITES, 2011 Lecture 1 20