PHY 1121 Physical Science

PHY 1121 Physical Science “Physics through Music” Examination #2 - SOLUTIONS

Here are the solutions to Exam #2. I was very lenient in what I accepted in the “essay” type questions. Please compare your answers to the answers below and if you find you deserved points that you didn’t get, please see me. If you were marked correct on a wrong answer, I leave your response up to you. I gave credit to everyone for question #2 because it appears that I didn’t make the answer very clear in class nor did I give it any emphases. (It was in the book!) I also added 5 points to shift the curve a bit. (A small bit). As I mentioned in the lecture, I will NOT adjust any of the grades this way in the future.

(1) Suppose that a string on a guitar sounds the tone A (440 Hz.). What is the frequency of a tone one octave higher? ANS ____880 Hz__

(2) What is the frequency of the first overtone above the A in question (1)? ANS ______880 Hz_

(3) If the speed of sound is 450 m/s, what is the wavelength of a tone sounding an A? f  velocity v 450     1.02m  440 ANS __1.02 M_____

(4) Describe what a Helmholtz resonator is and why it was important to the science of music: H created a series of bottles that resonated at various tones that could be compared to those of musical instruments. The siren, which created tones of known frequency could then be connected to the musical tones. So tones now had frequencies while before tey didn’t.

(5) What is the period of the A tone in problem (1)? 1 1 T    0.0022s f 440 ANS ___0.0022 sec

(6) Consider a spring whose spring constant is 100 N/m supporting a mass of 2 Kg. What is the resonant frequency for this combination? 1 k 1 100 7.1 f     1.125 2 m 2x3.14 2 6.28 ANS ___1.125 Hz

1 NAME ______

7) Consider a string of length L=1 meter that is fixed at both ends and that is under tension. In class, we discussed the fact that if we pulled the string down at its center it would respond with a force that was proportional to how far we pulled the string. Thus, it behaves like a spring. If the spring constant for the string is 50 N/m, what would the spring constant be for a string half this length?

We did the demo in class …. it doubled. (were you there? ANS ______100N/m_

The figure on the right shows a spring in its un- A O C stretched condition with a mass connected to it. The mass is pulled from its equilibrium condition (O) to point C and then released. The mass will then continue to oscillate from C-O-A-O-C-O etc. with no friction.

(9) At what position(s) is the kinetic energy of the mass a maximum? ANS _____O______

(10) At what positions(s) is the potential energy a maximum? ANS ______A,C____

(11) At what position(s) is the potential energy a minimum? ANS ______O_____ The last three were all conservation of energy.

The figure to the right shows the pressure at a particular point as a function of time. The pressure variations are due to sound.

(12) The dashed curve represents

(a) the louder of the two pressure waves shown. (b) the lower of the two pressure waves shown. (c) the higher frequency of the two pressure waves shown. (d) the lower frequency of the two pressure waves shown. (e) there is not enough information supplied to answer this question.

Both have the same frequency (repeat together) but different heights or levels of loudness.

ANS ______(b)___

2 NAME ______

(13) A woman pushes a 12,000 Kg mass through a distance of 5 meters. How much work did she do? (Take g=9.8 ms/2) (a) 60,000 Joules (b) 60,000 Newtons (c) 58,800,000 Joules (d) None of these W  Fd . The force wasn’t given so none of the answers are correct. ANS _____D______

(14) A 5 kg mass is hovering over the ground at height of 10 meters. What is its potential energy? PE  mgh  5 9.810  490J . Most of you left out the g! ANS __490J______

(15) If the mass should be released, what would its Kinetic Energy be when it hits the ground? Same answer because the energy was conserved. Some wise guys said zero because it wasn’t moving after it hit the ground. This is also a correct answer but not the one I expected!. ANS ___490 J_____

3 Consider the photograph of a guitar:

(16) Fill in the following table:

IDENTITY NAME OF PART FUNCTION A Face, Box or Amplifies the sound of the strings vibration and Resonator. sends it into the room.

B Strings The vibrator.

C Frets Allows the length of a string to be changed so that the tone can be changed.

D The bridge Transfers the energy of the string to the guitar box or resonator.

(17) What is a standing wave and how is it created?

_A standing wave is the result of two identical waves moving in opposite directions. I was looking for a description of the nodes and anti-nodes which are the main properties of the standing wave. Anything even close to this was accepted. ______

4 (18) If the tension in a string is quadrupled, the velocity of a transverse wave on the string is (a) halved (b) doubled (c) multiplied by 4 (d) is unchanged tension If T is quadrupled, we have the square root of 4T which is is twice mass / unit  length the original number. ANS ______B_____

(19) The velocity of a wave traveling on a guitar string is the same as the velocity of the sound wave that it produces. Briefly discuss this statement.

__The velocity of sound is completely independent of frequency or anything else for that matter. The velocity of the wave on the string (see formula) changes as the tension is changed. The velocity would increase on the string but the velocity of the sound that it emits would remain the same 450 m/s. ______

(20) What makes different stringed instruments sound different?

_I was looking for Timbre, or a different combination of harmonics.______

(21) The following diagram shows a wave on a string that is fixed at the wall. Sketch what the reflected wave looks like.

5 (22) Explain why your diagram looks the way it does.

See the notes of either of the books. As the wave approaches, it starts to push UP on the rope. Newton’s third law says the wall will push DOWN so the shape is inverted. ______

Sorry this gave you so much trouble!

6 “Physics through Music”

EQUATIONS PROVIDED IN EXAMINATION II OCTOBER 22, 2004

You must know what these equations refer to and what they mean.

Period of an Oscillator = time per oscillation Frequency of an oscillator = number of oscillations per second f=1/T or fT=1 For a spring, the force F is given by F= -kx

The period of an oscillating mass at the end of a sprig, f , is given by 1 k f  2 m ENERGY: Work is a force times the distance through which the force acted:

Work = Force x Distance

momentum = mv momentum is “conserved” in a collision (know what that means)

If something hits a wall and bounces back, the wall applies a Force over a period of time that changes the momentum of the particle. Momentum is ONLY conserved when there are no external forces. So,

F t = change of momentum = 2 x initial momentum

The kinetic energy of an object is KE = (1/2) mv2 and we then decided that ENERGY IS CONSERVED, meaning that the total energy before a collision is equal to the total energy after the collision. Consequently sound from a crash takes some energy away from the total. We call this noise, but if a drum stick hits a drum, it becomes something related to music.

We then LIFTED an object from an initial reference level to a final level and called the energy POTENTIAL energy. Based upon the definition of how much work is done on an object when it is lifted through a height h, we defined the PE as:

PE = mgh and PE counts in the energy conservation equation!

7 So the energy before a collision of an object (KE + PE) = total amount of energy available after the collision (KE + PE + losses due to heat, friction, sound, etc.)

The potential energy of a SPRING was found to be 1 PotentialEnergy  PE  kx 2 spring spring 2

The period of a pendulum was also mentioned: l T  2 g WAVES: tension Velocity of a wave on a string = mass / unit  length