Periodic Motion Problems - Assignment Example

? For a massive block oscillating up and down on a spring like in Fig 9 5, label how the following changes would affect the oscillation period. Label it as making it shorter (S), longer (L), or unchanged (U). Explain your response. a. Reducing the mass. (S) The force applied on the spring reduces hence the tension. The spring therefore accelerate mass faster, therefore the period would be shorter. b. Taking it to the moon where gravity is weaker. (U) The gravity change would have no effect on the period taken since the mass and spring are still the same, therefore no change is expected. c. Weakening the spring (reducing the spring constant). (L) For a weakened spring, the force the spring exerts is decreased. The oscillations period would be therefore lengthened, would be longer d. Making the amplitude of the oscillation larger.(U) The amplitude does not affect frequency since the distance from relaxation position would increase the restoring force. Therefore, the frequency remains unchanged. 2. For a pendulum as in Fig 9.1.2: label how the following changes would affect the oscillation period. Label each as making the period shorter (S), longer (L), or unchanged (U). Explain your response. a. Taking it to a planet where gravity is larger.(S) Gravity affects the oscillation period from the formula of finding period using length and gravity. Therefore, as the gravity increases, the period decreases as they are inversely proportional b. Increase the mass hanging on the pendulum.(U) Period is mass independent. Therefore, at gravity all masses accelerate equally, hence the period is unchanged. c. Making the pendulum shorter. (S) The length is directly proportional to the period. Therefore a decrease in the pendulum length decreases the period d. Reducing the amplitude of the oscillation (assuming that it was not very big to start with). (U) The oscillations period remains constant due to the lack of relation to the amplitude. 3. The frequency of the tone produced by a violin string is higher (H), lower (L) or unchanged (U) if we make the following changes (note that here we are asking about the frequency, whereas on the earlier problems we were asking about the period of the oscillation, which is just the inverse of the frequency) : a. Making the string shorter. (H) The frequency of the tone is high. The shorter the string the higher the pitch, therefore the high frequency experienced. b. Making the string thicker. (L) The increased thickness increases the mass per unit length. Therefore the string moves slower which decreases the pitch, hence the frequency. c. Pressing the string down on the fingerboard.(H) The vibration reduces when the spring is pressed to the fingerboard; the active part is shortened. Therefore the pitch and frequency rose. d. Reducing the tension of the string. (L) The reduced tension of string causes slow movement of the string therefore the pitch and frequency reduced Explain your response. 4. I take a violin and make an exact copy of it, except that it is bigger. The strings are identical except for the length; they have the same material and the same tension. If the new violin is 2.30 times the size of the original, at what frequency would the string that was previously the A4 string (that is 440 Hz on a regular violin) oscillate? Use units of "Hz." Explain your response. When the size increases the pitch decreases, therefore 440Hz divided by 2.3 440Hz / 2.3= 191.30Hz 5. If your hearing cuts off at 17440 Hz, what is the highest harmonic of E5 string you can hear? The answer is an integer without units. Hint: The E5 string vibrates at 660 Hz. Explain your response. The highest harmonic is 17440Hz divided by 660Hz 17440/660=26.42 Rounding off, the highest harmonic to be heard is the 26th Harmonic 6. The frequency of the sound coming from the organ pipe is higher (H), lower (L) or the same (S) if we make the following changes to the organ: a. Moving the organ to a higher elevation. (H) The air is less dense at higher elevation, therefore the molecules move more freely. Therefore the pitch and frequency increases b. Making pipe longer. (L) The longer the pipe the lower the pitch just as in the case of long strings c. Blowing more air across the pipe.(S) The blowing does not change the frequency despite making it louder d. Exciting a harmonic of the pipe rather than fundamental mode. (H) The harmonics are higher Explain your response. 7. Label the following statements as true (T) or false (F). Explain your responses. a. Wrapping steel piano strings with fine copper wire will reduce the pitch.(T) When the strings are wrapped their mass per unit length is increased, therefore the strings move more slowly decreasing their pitch b. A violin string can only produce a single frequency unless the tuning is changed. (F) The harmonics can be excited for the effects to be produced c. As a violin string vibrates, its motional energy is changing rapidly with time.(T) The change is observable as it occurs d. High pitched violin strings are the most likely to break.(T) High pitched strings have least mass per unit length; very thin, therefore they are likely to break or snap. e. Most of the sound from a violin comes directly from the strings. (F) The sound in the violin is identified to come mostly from the belly 8. The global positioning system (GPS) uses clocks to tell you wherever you are on earth to within several feet. The GPS is a bunch of very accurate atomic clocks that are in satellites whose positions are well known. They send out radio pulses at very precise times, and a GPS receiver detects the time it takes for the pulses from all the different satellites to reach it. This tells it how far it is from each of the satellites. Then it does a bunch of fancy geometry to figure out its position. Let’s consider just one satellite so you do not have to do any geometry. You are somewhere in the middle of the country and a satellite that is a short distance above San Francisco sends out a pulse that your GPS receiver tells you took 0.002 seconds to reach you. Since you know that the radio signal travels at the speed of light, how far does this mean you are from San Francisco (neglect the distance between San Francisco and the satellite)? Explain your response. The speed of light is 3.0 x 108 m/s Therefore the distance is velocity x time Distance = 3.0 x108 x 0.002 6.0 x 105 9. Which of the following objects could be used to construct a functional clock? a. A super ball bouncing up and down many times on a hard floor. (F) The super ball looses energy as it bounces much faster, therefore it would not be used to effectively construct a functional cock b. A very low frequency tuning fork. (T) The frequency of the tuning fork is kept at a constant at a longer period; looses energy more slowly. It would be effectively used to construct a functional clock. c. A ribbon fluttering back and forth in the wind. (F) The motion and frequency by the ribbon is not constant it fluctuates highly. Therefore, it would not serve as an effective functional clock d. A car that is bouncing up and down as it drives over a bumpy road.(F) The bumps are unevenly distributed, therefore it would not be easy to predict the period of oscillations. e. A chair hanging by a bungee cord out a window.(T) The system is more of a spring and weight hang on it, therefore it would serve as a clock. 10. If a violin string is stretched out with a certain tension and then glued between two concrete pillars, what change would there be in the sound it produced when bowed compared to when it was attached with the same tension to a violin? a. It would produce a higher frequency. (F) Frequency is affected by tension, length, and string mass. Therefore the pitch would be the same b. It would produce fewer harmonics.(F) From the above description it would not be expected for the number of harmonics to change. c. It would give a much quieter sound. (T) The sound would be quieter since it is not carried through the belly. d. The string would move much less. (F) The motion would be constant e. It would produce a much louder sound. (F) As explained that the sound would be quieter References Giordano, N. (2010) College Physics: Reasoning and relationships. Belmont, CA: Cengage Learning Read More