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====== Differences ====== This shows you the differences between two versions of the page.
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exam_1_review [2014/04/19 07:11] wikimanager |
exam_1_review [2014/04/19 19:26] (current) wikimanager [Review problem 1] |
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| * a) Which of these waves travel in the $+x$ direction? (3 pts) | * a) Which of these waves travel in the $+x$ direction? (3 pts) | ||
| + | * <color green>waves 1 and 4 </color> | ||
| + | * <color green>(look for opposite signs in front of the //x// and //t// terms inside the cos or sin function)</color> | ||
| * b) Which of these waves have the same wavelength as wave 1? (3 pts) | * b) Which of these waves have the same wavelength as wave 1? (3 pts) | ||
| + | * <color green>wave 4 </color> | ||
| + | * <color green>(look for the same magnitude of the coefficient in front of //x// inside the cos or sin function)</color> | ||
| * c) Which of these waves have the same amplitude as wave 2? (3 pts) | * c) Which of these waves have the same amplitude as wave 2? (3 pts) | ||
| + | * <color green>wave 5 </color> | ||
| + | * <color green>(look for the same magnitude of the coefficient in front of the cos or sin function)</color> | ||
| * d) Which of these waves have the same period as wave 3? (3 pts) | * d) Which of these waves have the same period as wave 3? (3 pts) | ||
| + | * <color green>wave 1 </color> | ||
| + | * <color green>(look for the same magnitude of the coefficient in front of //t// inside the cos or sin function)</color> | ||
| * e) Which of these waves have the same speed as wave 4? (3 pts) | * e) Which of these waves have the same speed as wave 4? (3 pts) | ||
| + | * <color green>wave 5 </color> | ||
| + | * <color green>(look for the same magnitude of the ratio of the coefficients in front of //t// and in front of //x// inside the cos or sin function)</color> | ||
| + | |||
| + | <color blue>See [[start#equation_sheet_ch14|Equation sheet for Ch. 14, bullet #6]] for details...</color> | ||
| + | |||
| + | ===All of the parameters for each wave are summarized below=== | ||
| + | ^ Wave ^ Direction ^ Amplitude (m) ^ Wavelength (m) ^ Period (s) ^ Frequency (Hz) ^ Magnitude of speed $\left(\frac{\mathbf m}{\mathbf s}\right)$ ^ | ||
| + | | 1 | $+x$ | 0.12 | $\frac{2\pi}{3}$ | $\frac{2\pi}{21}$ | $\frac{21}{2\pi}$ | 7 | | ||
| + | | 2 | $-x$ | 0.15 | $\frac{\pi}{3}$ | $\frac{\pi}{21}$ | $\frac{21}{\pi}$ | 7 | | ||
| + | | 3 | $-x$ | 0.13 | $\frac{\pi}{3}$ | $\frac{2\pi}{21}$ | $\frac{21}{2\pi}$ | 3.5 | | ||
| + | | 4 | $+x$ | 0.27 | $\frac{2\pi}{3}$ | $\frac{\pi}{6}$ | $\frac{6}{\pi}$ | 4 | | ||
| + | | 5 | $-x$ | 0.15 | $\frac{2\pi}{9}$ | $\frac{\pi}{18}$ | $\frac{18}{\pi}$ | 4 | | ||
| ---- | ---- | ||
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| {{ :figs:ex1rev2.jpg?nolink&189|}} A musician (Andrew Bird) used a double spinning horn speaker during a recent tour. While one horn spins toward you, the other spins away. Say the horns are emitting a frequency of 880 Hz, are spinning with an angular velocity of 2.0 rad/s, and that each horn is 1.0 m long. | {{ :figs:ex1rev2.jpg?nolink&189|}} A musician (Andrew Bird) used a double spinning horn speaker during a recent tour. While one horn spins toward you, the other spins away. Say the horns are emitting a frequency of 880 Hz, are spinning with an angular velocity of 2.0 rad/s, and that each horn is 1.0 m long. | ||
| * a) Due to a Doppler shift, what is the greatest pitch (frequency $f$) you will hear? Will this be when the horn is spinning towards you or away from you? (Remember, $v_t = A\omega$, where $A$ is the distance from the rotation axis to the opening of the horn) (3 pts) | * a) Due to a Doppler shift, what is the greatest pitch (frequency $f$) you will hear? Will this be when the horn is spinning towards you or away from you? (Remember, $v_t = A\omega$, where $A$ is the distance from the rotation axis to the opening of the horn) (3 pts) | ||
| + | * <color green>Greatest pitch - motion towards you</color> | ||
| + | * <color green>$f'=f\left(\frac{1}{1-\frac{u}{v}}\right)$ $=f\left(\frac{1}{1-\frac{A\omega}{v}}\right)$ $=880\,{\text{Hz}}\,\left(\frac{1}{1-\frac{1.0\,{\text m}\,\cdot\,2.0\,\frac{\text{rad}}{\text s}}{340\,\frac{\text m}{\text s}}}\right)$ $=885\,$Hz </color> | ||
| * b) What is the lowest pitch you will hear from the speakers due to a Doppler shift? Will this be when the horn is spinning towards you or away from you? (3 pts) | * b) What is the lowest pitch you will hear from the speakers due to a Doppler shift? Will this be when the horn is spinning towards you or away from you? (3 pts) | ||
| + | * <color green>Lowest pitch - motion away from you</color> | ||
| + | * <color green>$f'=f\left(\frac{1}{1+\frac{u}{v}}\right)$ $=f\left(\frac{1}{1+\frac{A\omega}{v}}\right)$ $=880\,{\text{Hz}}\,\left(\frac{1}{1+\frac{1.0\,{\text m}\,\cdot\,2.0\,\frac{\text{rad}}{\text s}}{340\,\frac{\text m}{\text s}}}\right)$ $=875\,$Hz </color> | ||
| * c) What is the beat frequency you hear from this instrument? (3 pts) | * c) What is the beat frequency you hear from this instrument? (3 pts) | ||
| + | * <color green> $f_\text{beat}=\big|\,f_1-f_2\big|$ $=\big|885\,{\text{Hz}}-875\,{\text{Hz}}\big|$ $=10\,$Hz </color> | ||
| * d) At the concert your friend sitting 1 m from the speakers hears an intensity of $9.0\times 10^{-2}\frac{\text W}{\,{\text m}^2}$. What intensity do you hear sitting 10 m away from the speakers? (3 pts) | * d) At the concert your friend sitting 1 m from the speakers hears an intensity of $9.0\times 10^{-2}\frac{\text W}{\,{\text m}^2}$. What intensity do you hear sitting 10 m away from the speakers? (3 pts) | ||
| + | * <color green> $I=\frac{\text{Power}}{4\pi r^2}$ </color> | ||
| + | * <color green> $\frac{I_\text{friend}}{I_\text{you}}=\frac{(10\,{\text m})^2}{(1\,{\text m})^2}$ $=100$ </color> | ||
| + | * <color green> $I_\text{you}=\frac{1}{100}I_\text{friend}$ $=9.0\times 10^{-4}\frac{\text W}{\,{\text m}^2}$ </color> | ||
| * e) What is the intensity level in decibels that your friend hears? (3 pts) | * e) What is the intensity level in decibels that your friend hears? (3 pts) | ||
| + | * <color green> $\beta=10\,{\text{dB}}\log\left(\frac{I_1}{I_\text{t.h.}}\right)$ $=10\,{\text{dB}}\log\left(\!\frac{9.0\times 10^{-2}\frac{\text W}{\,{\text m}^2}}{ 10^{-12}\frac{\text W}{\,{\text m}^2}}\!\right)$ $\approx 110\,$dB </color> | ||
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| - Two sources that emit crests at the same time and emit troughs at the same time. | - Two sources that emit crests at the same time and emit troughs at the same time. | ||
| + | * <color green>In-phase sources</color> | ||
| - Ninety degrees to both the electric field and the magnetic field in a moving electromagnetic wave. | - Ninety degrees to both the electric field and the magnetic field in a moving electromagnetic wave. | ||
| + | * <color green>Direction of propagation of light</color> | ||
| - Energy per unit time per unit area. | - Energy per unit time per unit area. | ||
| + | * <color green>Intensity</color> | ||
| - A measure of sound intensity. Increasing by about three of these units will indicate a doubling of the intensity of the sound. | - A measure of sound intensity. Increasing by about three of these units will indicate a doubling of the intensity of the sound. | ||
| + | * <color green>Decibel</color> | ||
| - When two waves combine to create a wave with an amplitude less than either of the two original waves. | - When two waves combine to create a wave with an amplitude less than either of the two original waves. | ||
| + | * <color green>Destructive interference</color> | ||
| - A part of the electromagnetic spectrum with frequencies just greater than those visible by humans. | - A part of the electromagnetic spectrum with frequencies just greater than those visible by humans. | ||
| + | * <color green>Ultraviolet</color> | ||
| - A point mass on the end of a mass-less string that is allowed to swing back and forth. | - A point mass on the end of a mass-less string that is allowed to swing back and forth. | ||
| + | * <color green>Simple pendulum</color> | ||
| - A wave where the direction of the molecules is perpendicular to the direction of the wave. | - A wave where the direction of the molecules is perpendicular to the direction of the wave. | ||
| + | * <color green>Transverse wave</color> | ||
| - The lowest frequency that can be created on a string or in a tube. | - The lowest frequency that can be created on a string or in a tube. | ||
| + | * <color green>Fundamental frequency</color> | ||
| - The length of time between two wave crests. | - The length of time between two wave crests. | ||
| + | * <color green>Period</color> | ||
| ---- | ---- | ||
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| The air pressure variations in a sound wave cause the eardrum (tympanic membrane) to vibrate. | The air pressure variations in a sound wave cause the eardrum (tympanic membrane) to vibrate. | ||
| - For a given vibration amplitude, are the maximum velocity and acceleration of the eardrum greatest for high frequency sounds or low frequency sounds? (1 pts) | - For a given vibration amplitude, are the maximum velocity and acceleration of the eardrum greatest for high frequency sounds or low frequency sounds? (1 pts) | ||
| + | * <color green>$v_\text{max}$ $=x_\text{max}\omega$</color> | ||
| + | * <color green>$a_\text{max}$ $=x_\text{max}\omega^2$</color> | ||
| + | * <color green>the greatest values are for the high-frequency sound</color> | ||
| - Find the maximum velocity and the maximum acceleration of the eardrum for vibrations of amplitude $1.0\times 10^{-8}\,$m at a frequency of 20.0 kHz. (5 pts) | - Find the maximum velocity and the maximum acceleration of the eardrum for vibrations of amplitude $1.0\times 10^{-8}\,$m at a frequency of 20.0 kHz. (5 pts) | ||
| + | * <color green>$v_\text{max}$ $=x_\text{max}\omega$ $=x_\text{max}(2\pi f)$ $=1.0\times 10^{-8}\,$m$\,\cdot\,6.283\cdot 20\times 10^3\,$Hz $=1.26\times 10^{-3}\frac{\text m}{\text s}$ </color> | ||
| + | * <color green>$a_\text{max}$ $=x_\text{max}\omega^2$ $=x_\text{max}(2\pi f)^2$ $=1.0\times 10^{-8}\,$m$\,\cdot\,(6.283\cdot 20\times 10^3\,$Hz$)^2=158\,\frac{\text m}{\,{\text s}^2}$ </color> | ||
| - What is the period of a complete oscillation of the ear drum at this frequency? (2 pts) | - What is the period of a complete oscillation of the ear drum at this frequency? (2 pts) | ||
| + | * <color green>$T=\frac{1}{f}$ $=\frac{1}{20\times 10^3\,{\text{Hz}}}$ $=5.0\times 10^{-5}\,$s</color> | ||
| - Using a crude model of the eardrum as a mass (3.0 mg) on a spring, what would be the spring constant of the eardrum, assuming the resonance frequency of 20.0 kHz? (3 pts) | - Using a crude model of the eardrum as a mass (3.0 mg) on a spring, what would be the spring constant of the eardrum, assuming the resonance frequency of 20.0 kHz? (3 pts) | ||
| + | * <color green>$T=2\pi\sqrt{\frac{m}{k}}$</color> | ||
| + | * <color green>$\left(\frac{T}{2\pi}\right)^2=\frac{m}{k}$</color> | ||
| + | * <color green>$k=\frac{4\pi^2m}{T^2}$ $=\frac{4\,\cdot\,3.14159^2\,\cdot\,3.0\times 10^{-6}\,{\text{kg}}}{\big(5.0\times 10^{-5}\,{\text s}\big)^2}$ $=4.74\times 10^4\frac{\text N}{\text m}$</color> | ||
| - The ear canal (external auditory canal) can be modeled as a tube with one closed end. If the length of the ear canal is 25 mm long and the speed of sound in air is 340 m/s, what is the fundamental (1<sup>st</sup> harmonic) of the ear canal? (4 pts) | - The ear canal (external auditory canal) can be modeled as a tube with one closed end. If the length of the ear canal is 25 mm long and the speed of sound in air is 340 m/s, what is the fundamental (1<sup>st</sup> harmonic) of the ear canal? (4 pts) | ||
| + | * <color green>$f_1=\frac{v}{4L}$ $=\frac{340\,\frac{\text m}{\text s}}{4\,\cdot\,25\times 10^{-3}\,{\text m}}$ $=3400\,$Hz</color> | ||
exam_1_review.1397891506.txt.gz ยท Last modified: 2014/04/19 07:11 by wikimanager
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