Oscillatory Motion and Waves

(a) A photovoltaic array of (solar cells) is 10.0% efficient in gathering solar energy and converting it to electricity. If the average intensity of sunlight on one day is 700 W/m², what area should your array have to gather energy at the rate of 100W? (b) What is the maximum cost of the array if it must pay for itself in two years of operation averaging 10.0 hr per day? Assume that it earns money at the rate of 9.00C per kilowatt-hour.

Describe a system in which elastic potential energy is stored.

What conditions must be met to produce simple harmonic motion?

(a) If the frequency is not constant for some oscillation, can the oscillation be simple harmonic motion?

(b) Can you think of any examples of harmonic motion where the frequency may depend on the amplitude?

Give an example of a simple harmonic oscillator, specifically noting how its frequency is independent of amplitude.

Explain why you expect an object made of a stiff material to vibrate at a higher frequency than a similar object made of a spongy material.

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.

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

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, with other factors remaining constant? Explain your answer.

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.)

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

 How would a car bounce after a bump under each of these conditions?

 • Over damping

 • Under damping 

• Critical damping

Most harmonic oscillators are damped and, if undriven, eventually come to a stop. How is this observation related to the second law of thermodynamics?

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

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.

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

Speakers in stereo systems have two color-coded terminals to indicate how to hook up the wires. If the wires are reversed, the speaker moves in a direction opposite that of a properly connected speaker. Explain why it is important to have both speakers connected in the same way.

Two identical waves undergo pure constructive interference. Is the resultant intensity twice that of the individual waves? Explain your answer.

Circular water wavCircular water waves decrease in amplitude as they move away from where a rock is dropped. Explain why.es decrease in amplitude as they move away from where a rock is dropped. Explain why.

What is the period of 60 Hz electrical power?

Find the frequency of a tuning fork that takes 2.50 x 10^-3 s to complete one oscillation.

A stroboscope is set to flash every 8 x 10^-5 s. What is the frequency of the flashes?

If the spring constant of a simple harmonic oscillator is doubled, by what factor will the mass of the system need to change in order for the frequency of the motion to remain the same?

By how much leeway (both percentage and mass) would you have in the selection of the mass of the object in the previous problem if you did not wish the new period to be greater than 2.01 s or less than 1.99 s?

A car has two horns, one emitting a frequency of 199 Hz and the other emitting a frequency of 203 Hz. What beat frequency do they produce?

The middle-C hammer of a piano hits two strings, producing beats of 1.50 Hz. One of the strings is tuned to 260.00 Hz. What frequencies could the other string have?

Two tuning forks having frequencies of 460 and 464 Hz are struck simultaneously. What average frequency will you hear, and what will the beat frequency be?

Twin jet engines on an airplane are producing an average sound frequency of 4100 Hz with a beat frequency of 0.500 Hz. What are their individual frequencies?

A microphone receiving a pure sound tone feeds an oscilloscope, producing a wave on its screen. If the sound intensity is originally 2.00 x 10^-5  W/m², but is turned up until the amplitude increases by 30.0%, what is the new intensity?

(a) What is the intensity in W/m² of a laser beam used to burn away cancerous tissue that, when 90.0% absorbed, puts 500 J of energy into a circular spot 2.00 mm in diameter in 4.00 s? 

(b) Discuss how this intensity compares to the average intensity of sunlight (about 700 W/m²) and the implications that would have if the laser beam entered your eye. Note how your answer depends on the time duration of the exposure.