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### Learning object: wave speed relationships

• 2. How quickly do waves move through a medium?  The speed at which a wave propagates through a medium depends on the properties of the medium  higher tension in string = greater wave speed  Denser materials = greater wave speed Speed in solid metal Speed in water Speed in air
• 3.  Waves cause a disturbance to the medium that they are travelling through  As the wave moves the particles in the medium, there is a restoring force trying to move the particles back to where they were originally  The more quickly the particles respond to the wave, the greater the restoring force You can visualize this by considering the distance between particles. Since there is so much space between the particles in air, it takes extra time before one particle affected by a sound wave reaches another particle and passes on the energy. In a solid, the particles are almost touching so the wave is propagated almost immediately.
• 4. Examples of the speed of sound waves in some different media: Vair: 343 m/s Vwater: 1400 m/s Vsteel: 6000 m/s When in the SAME MEDIUM, all sound waves travel at the same speed. A higher frequency, louder wave and a lower frequency, quieter wave both travel in air at 343 m/s.
• 5. Key Equation: v = fλ  Wave speed is equal to wave frequency times wavelength  Wave frequency is how many cycles per second (Hertz)  Wave length is distances between two crests or two troughs of adjacent waves (m)  As long as the wave stays in one medium, speed is constant, so:  If frequency increases, wavelength decreases, and vice versa
• 6.  Dolphins “see” in water by producing very rapid clicks (sound waves) and listening for the echoes of these sound waves bouncing off objects.  A part of the dolphin brain can “calculate” distance to the object by using the expected wave speed through water and half the time it takes for the echo to return to the dolphin.
• 7. Some practice questions: 1. The normal range of frequencies at which dolphins use echolocation is from 0.2 kHz to 150 kHz. Determine the periods and wavelengths of the upper and lower frequency limits. (Assume speed of sound waves in shallow salt water is 1485 m/s.) 2. How far away is a herring fish (that the dolphin wants to eat) if the dolphin hears the echo 0.078 s after producing its clicks? 3. The increase in pressure as a dolphin dives deeper causes a slight change in the speed of sound waves (suppose that every 100 m increase in depth causes wave speed to change by 1.56 m/s). If the dolphin brain is hard-wired to use 1485 m/s as the wave speed, what is the percentage error in the dolphin’s perceived location of a herring fish 83 m away when the dolphin has dived 260 m deeper than normal? Is this a big deal for the dolphin?
• 8. Solutions: 1. To find period, use T = 1/f. To find wavelength, use V= fl. Remember to convert the values given in kiloHertz to Hertz! For 0.20 kHz, T = 0.0050 s, l = 7.4m. For 150 kHz, T = 0.0000067 s, l = 0.0099 m or 9.9 mm. 2. Time for sound wave to reach fish and come back is 0.078s, so the time it takes for sound to just reach the fish is 0.039 s. Speed times time equals distance, so (0.039 s)(1485 m/s) = 58 m. 3. First recognize that as materials become denser, wave speed tends to increase, so the change in wave speed in the question means an increase of 1.56 m/s with every 100 m of depth. To find the new wave speed, divide 260m by 100 m to get 2.6, and multiply 2.6 by the +1.56 m/s to get an increase in speed of 4.1 m/s. Use the new total wave speed of 1489.1 m/s and the distance to the fish to find how long the echoes ACTUALLY take to reach the fish and come back, and multiple this time with the hardwired wave speed of 1485 m/s to find the perceived distance. The actual distance is 83 m, the perceived turns out to be 82.77. This is rather close and should not be a problem for the dolphin.
• 9. Bibliography "Bottlenose Dolphins Communication & Echolocation." SeaWorld.org. SeaWorld Parks and Entertainment, n.d. Web. 8 Feb. 2015.
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