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_{PH203KUZMASPRING2015}
Video 2.1: Ruben's tube, standing wave with explanation. | Video 2.2: Standing waves on a 2D surface. |
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video 2.3: doppler effect, shock wave , and sonic boom |
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From: Walker, James S. “Ch. 14 Waves and Sound.” Physics. Upper Saddle River, NJ: Pearson/Prentice Hall, 2004
Table 14.1: Speed of sound in various materials | ||
Material | Temperature | Speed of sound (m/s) |
---|---|---|
Aluminum | 6420 | |
Granite | 6000 | |
Steel | 5960 | |
Pyrex glass | 5640 | |
Copper | 5010 | |
Plastic | 2680 | |
Fresh water | 20 $^\circ$C | 1482 |
0 $^\circ$C | 1402 | |
Hydrogen | 0 $^\circ$C | 1284 |
Helium | 0 $^\circ$C | 965 |
Air | 20 $^\circ$C | 343 |
0 $^\circ$C | 331 |
Addition of trig functions | Doppler equation approximation for slow observer/source speeds $u\ll v$ | |||
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$\sin\alpha+\sin\beta=$ $2\sin\left(\frac{\alpha+\beta}{2}\right)\cos\left(\frac{\alpha-\beta}{2}\right)$ | $\left(1+\frac{u}{v}\right)^2$ $\approx 1+2\frac{u}{v}$ | $\left(1-\frac{u}{v}\right)^2$ $\approx 1-2\frac{u}{v}$ | ||
$\cos\alpha+\cos\beta=$ $2\cos\left(\frac{\alpha+\beta}{2}\right)\cos\left(\frac{\alpha-\beta}{2}\right)$ | $\left(1+\frac{u}{v}\right)\left(1-\frac{u}{v}\right)$ $\,=\, 1-\left(\frac{u}{v}\right)^2$ $\,\approx\, 1$ | $\left(1+\frac{u_1}{v}\right)\left(1-\frac{u_2}{v}\right)$ $\approx 1+\frac{u_1-u_2}{v}$ | ||
$\cos\alpha+\sin\beta=$ $-2\sin\left(\frac{\alpha+\beta}{2}+\frac{\pi}{4}\right)\sin\left(\frac{\alpha-\beta}{2}-\frac{\pi}{4}\right)$ | $\left(\frac{1}{1+\frac{u}{v}}\right)$ $\approx 1-\frac{u}{v}$ | $\left(\frac{1}{1-\frac{u}{v}}\right)$ $\approx 1+\frac{u}{v}$ | ||
$\cos\alpha-\cos\beta=$ $-2\sin\left(\frac{\alpha+\beta}{2}\right)\sin\left(\frac{\alpha-\beta}{2}\right)$ | $\left(\frac{1+\frac{u}{v}}{1-\frac{u}{v}}\right)$ $\approx 1+2\frac{u}{v}$ | $\left(\frac{1-\frac{u}{v}}{1+\frac{u}{v}}\right)$ $\approx 1-2\frac{u}{v}$ | $\left(\frac{1+\frac{u_1}{v}}{1-\frac{u_2}{v}}\right)$ $\approx 1+\frac{u_1+u_2}{v}$ |
Please update if an equation is not included
What is the wavelength of the lowest and the highest frequency you can hear?
Steps:
Estimate the frequency of the “EE” sound.
If one can't (almost) hear an airplane 35,000 ft above, how close can one stand next to this source of noise without feeling pain?
Assuming the power is constant, use the ratio of the threshold of pain to threshold of hearing to solve for the distance of the threshold of pain. The distance for the threshold of hearing is given. (r_{h} = 35,000 ft = 10,668 m)
Steps:
A mountaineer, whose mass (including gear) is 250 lb, is hanging next to the face of a cliff in total fog, suspended by a 24-lb, 600-ft kernmantle rope, tied to his buddy above. What is the delay in perception of the buddy's movements (hammering nails into the rock) sensed by the mountaineer through the rope?
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A string on a violin, 60 cm in length, is tuned to the middle A ($f_1 = 440\,$Hz) by applying 14 lb of tension. Find the mass of the string.
Steps:
In a problem like this, will we need to calculate the speed of sound at a given temperature or will that number be provided? — Thomas Ruttger 2015/04/20 21:31
Organ pipe (one end closed, one open) is tuned to $f_1=440\,$Hz at 20$\,^\circ$C
Steps:
You are listening to an echo while playing a 440-Hz note and biking at 20 mph towards a wall. Find the frequency of the echo.
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The peak blood velocity in fetal aorta is about $20\,\frac{\text{cm}}{\text s}$. If one images it using a 9 MHz ultrasound, find the maximum Doppler frequency shift of the echo at the detector. Assume the speed of sound in the body v = 1500 m/s. (The blue and red colors in the video represent the blood flow in the ultrasound image moving either towards or away from the detector. The long stripes of alternating white and gray blobs are the baby's spine, and/or the ribs penetrating the imaging plane.)
Steps: