Physics Exam #3

What is the difference between propagation speed and the frequency of a wave? Does one or both affect wavelength? If so, how?

A wave is a disturbance in the medium caused due to any reason. The speed at which this disturbance moves is known as propagation speed. By frequency means the number of eents (cycles) per unit of time. Wave velocity and wavelength are related. The expression which shows the relation is: Vw = wavelength / period and Vw = frequency x wavelength

Give an example of a damped harmonic oscillator. (They are more common than undamped or simple harmonic oscillators.)

An example of a damped harmonic oscillator includes when the amplitude of oscillation gradually decreases and the system goes to rest. For instance, a hanging simple pendulum in the air is an example for this. The amplitude of the pendulum in air decreases slowly due to resistance to air molecules and the pendulum eventually will go to rest.

Why is the index of refraction always greater than or equal to 1?

Because it is defined as the speed of light in empty space, divided by the speed of light in a particular material. The speed of light can only decrease as density increases and vacuum is the least dense medium we can think of.

What conditions must be met to produce simple harmonic motion?

Conditions to produce simple harmonic motion include that the net force must be described by F=-kx, where F is the restoring force, x is the displace, and k is the force constant. To produce simple harmonic motion, the rate of change of velocity must be proportional to the displacement.

Explain in terms of energy how dissipative forces such as friction reduce the amplitude of a harmonic oscillator. Also explain how a driving mechanism can compensate. (A pendulum clock is such a system.)

For the harmonic oscillator, the law of conservation of energy is followed, which results in the amplitude of the system remaining constant. Dissipative forces, such as friction, result in some energy being lost in different forms of energies and leads to a decrease in amplitude after each oscillation. This is because the sum of kinetic energy and potential energy decreases after each oscillation. For the driving mechanism, some external force acting on the system (driving force) must be accounted for and in this scenario, energy is lost due to dissipative forces that can be provided back to the system with the involvement of the driving force and makes up for the energy lost.

Give one example of a transverse wave and another of a longitudinal wave, being careful to note the relative directions of the disturbance and wave propagation in each.

For transverse waves the displacement of the medium is perpendicular to the direction of propagation of the wave. A ripple on a pond and a wave on a string are easily visualized transverse waves. In longitudinal waves the displacement of the medium is parallel to the propagation of the wave. A wave in a "slinky" is a good visualization. Sound waves in air are longitudinal waves.

As you pass a freight truck with a trailer on a highway, you notice that its trailer is bouncing up and down slowly. Is it more likely that the trailer is heavily loaded or nearly empty? Explain your answer.

If the freight truck with a trailer seems to be bouncing up and down slowly, it is more likely that the trailer is nearly empty rather than heavily loaded. This is because frequency of oscillation and mass of the system (the trailer) are inversely proportional given the relationship, f=(1/2)km. The trailer is probably nearly empty and that is why it seems to oscillate while driving on the highway.

Will light change direction toward or away from the perpendicular when it goes from air to water? Water to glass? Glass to air?

Law of refraction: If nr > ni, light bends toward normal If ni > nr, light bends away from normal

You are given two wind instruments of identical length. One is open at both ends, whereas the other is closed at one end. Which is able to produce the lowest frequency?

Looking at the equations for open and closed tubes, you can tell that the closed tube resonator will have the lower frequency due to the wavelength being divided by a greater number than the open tube.

How would a car bounce after a bump under each of these conditions? • overdamping • underdamping • critical damping

Overdamping in a system refers to when a system arrives at equilibrium at an exponential decay rate with no oscillations. In this case, the car bounces to a visible extent and would take longer to return to its equilibrium position/steady state on the road. Underdamping in a system refers to when oscillations occur with reduced frequency and the amplitude also gradually decreases. In this case, the car does not bounce to the same extent as it bounced in the overdamped scenario. The care will also arrive at is equilibrium state more quickly. Critical damping refers to when a system arrives at equilibrium very quickly with no oscillations. In this case, the car would bounce slightly and then immediately go to its equilibrium state.

What is the difference between an overtone and a harmonic? Are all harmonics overtones? Are all overtones harmonics?

Overtones refer to any resonant frequency of a system that has a frequency higher than its fundamental frequency. Harmonics refer to resonant frequencies which are integer multiples of the fundamental frequency. The lowest resonant frequency is called the fundamental, while all higher resonant frequencies are called overtones. no, all harmonics aren't overtones yes, all overtones are harmonics

How does an unamplified guitar produce sounds so much more intense than those of a plucked string held taut by a simple stick?

String instruments such as violins and guitars use resonance in their sounding boxes to amplify and enrich the sound created by their vibrating strings. The bridge and supports couple the string vibrations to the sounding boxes and air within The front face of an acoustic guitar is called the soundboard. The guitar's hollow body and the hole in the soundboard increase the efficiency further.

Why are soldiers in general ordered to "route step" (walk out of step) across a bridge?

Structures like bridges have a natural frequency of vibration within them. A force that's applied to an object at the same frequency as the object's natural frequency will amplify the vibration of the object in an occurrence called mechanical resonance.if soldiers march in unison across the structure, they apply a force at the frequency of their step If their frequency is closely matched to the bridge's frequency, the soldiers' rhythmic marching will amplify the vibrational frequency of the bridge. If the mechanical resonance is strong enough, the bridge can vibrate until it collapses from the movement thats why soldiers are in general ordered to "route step"

When you hear a sonic boom, you often cannot see the plane that made it. Why is that?

The plane is going faster than the speed of sound, therefore the plane had already passed by the time you hear the sonic boom.

When sound passes from one medium to another where its propagation speed is different, does its frequency or wavelength change? Explain your answer briefly.

The speed of sound can change when sound travels from one medium to another. However, the frequency usually remains the same because it is like a driven oscillation and has the frequency of the original source. If vw changes and f remains the same, then the wavelength λ must change. That is, because vw = fλ , the higher the speed of a sound, the greater its wavelength for a given frequency

Some people modify cars to be much closer to the ground than when manufactured. Should they install stiffer springs? Explain your answer.

These people should not install stiffer springs. Stiffer spring would not result in cars being much closer to the ground. The greater the stiffness in the spring, the greater the force constant, which will result in an increased restoring force. This restoring force is directly proportional to the spring constant given that F=-kx. The increased restoring force would instead result in the car staying away from the ground instead of being much closer to it.

Pendulum clocks are made to run at the correct rate by adjusting the pendulum's length. Suppose you move from one city to another where the acceleration due to gravity is slightly greater, taking your pendulum clock with you, will you have to lengthen or shorten the pendulum to keep the correct time, other factors remaining constant? Explain your answer.

To make sure the pendulum keeps the correct time, the length of the pendulum should be increased. The time period of a simple pendulum is proportional to the ratio of the length of acceleration due to gravity as follows: T=2Lg.In the new city where the acceleration due to gravity is slightly greater, the length of the pendulum should be increased to make sure that the ratio of the length to the acceleration due to gravity (L/g) remains unchanged.