set3-soln - Physics 1240 Homework 3 solutions Brief...

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Physics 1240 Homework 3 solutions Brief solutions to homework set #3. Your numbers will be different, but the idea is the same. I’m just using sample numbers here. 1. You are walking next to a large lake, and notice there are traveling waves moving across the lake, driven by the wind. You want to know how fast they’re traveling, but it’s tricky to estimate directly. Then you spot a duck bobbing up and down in the water about 30 m away from you. Being a sound and music student, you make some quick visual estimates: you see that the duck bobs up and down about once every 5.0 seconds. It is bobbing a total vertical distance of about 0.5 m up and down (from peak to trough.) You also see that when the duck is at a peak there is about 7.0 meters between it and the next peak. You guess the water temperature is about 15 o C, and air temperature is about 25 o C. How fast are the waves traveling? The wavelength is the peak-to-peak distance: λ = 7 m . The period is the time for one full oscillation: P = 5 s . The wave speed is than v = λ/P = 7 m / 5 s = 1.4 m/s. 2. A saxophone is playing a steady note of freqency 875 Hz. The temperature in the room is 28 o C. At a given moment in time, the pressure at your eardrum is at a maximum. How far away from your ear is the next high pressure region in the air? The distance from maximum to maximum is the wavelength. We can use that v = and rearrange so λ = v/f . To get the sound speed note that the temperature is 8 o C above room temperature, so the speed is v = 344 m/s + 0 . 6 m/(s o C) × 8 o C = 348.8 m/s. Therefore λ = v f = 348 . 8 m/s 875 /s = 0 . 4 m . 3. Ultrasound with a frequency of 4.2 MHz can be used to image internal organs of the human body. If the speed of sound in the body is the same as in salt water (1575 m/s), what is its wavelength, in millimeters, in the body? What are some advantages and disadvantages to using ultrasound in this way? What are a couple of other practical uses of ultrasound (besides medical imaging in the body?) How big are the objects you would like to resolve in the resulting images (like an organ?) Why did I ask you to convert to mm? Note that 1 MHz = 10
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set3-soln - Physics 1240 Homework 3 solutions Brief...

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