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exam_1_review

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exam_1_review [2014/04/19 07:43] wikimanager [Review problem 4] - solution |
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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exam_1_review.1397893438.txt.gz ยท Last modified: 2014/04/19 07:43 by wikimanager

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