PHYS 2133
Chapter 16 Problems

Chapter Objectives

  1. Understand the relationship between wavelength, wave speed, and frequency.
  2. Understand the dependence on the tension and mass per unit length for the speed of waves on a string.
  3. Understand the Doppler shift in frequencies for relative motion between two objects.
  4. Calculate the intensity of sound in decibels.

Conceptual Questions

  1. Electricity from the power plant is sent as an sinusoidal, alternating current. What is the average velocity of an electron in the wire? What is the average distance travelled by the electron over one oscillation?
  2. The tension in a guitar string is doubled. What happens to its period of oscillation if it is plucked in the middle?
  3. The tension in a taut string is doubled. What happens to the speed of any oscillatory wave on the string?
  4. A guitar string is replaced by a string that is twice as heavy per unit length. What happens to the frequency of oscillation of the lowest harmonic?
  5. One end of a string is tied to a wall. The other end is pulled tight and shaken up and down in a sinusoidal fashion with a period T. If the end is shaken with a period 2T, what happens to the shape of the wave induced in the rope?
  6. A "trick" showed in some old western movies is to put one's ear to a railroad track to listen for the train before it is heard through the air. Why could this possibly work?
  7. During a snow storm, it usually becomes eerily quiet outside. Why is this?
  8. A gag often pulled at parties is for someone to inhale helium and then speak in a very squeaky voice. Why does the person's voice increase in frequency?
  9. Astronomers often quote that most of the stars in the universe are moving away from our planet. They base this statement on an investigation of the light spectra from stars. How can they determine that this is true?

Selected Problems

  1. Tranverse waves with a speed of 50.0 m/s are to be produced on a stretched string.   A 5.00 meter length of string with a total mass of 0.0600 kg is used. (a) What is the required tension in the string? (b) Calculate the wave speed in the string if the tension is 8.0 N.
  2. Transverse waves travel at 20.0 m/s on a string that is under a tension of 6.00 N. What tension is required for a wave speed of 30.0 m/s in the same string?
  3. A group of hikers hear an echo 3.0 s after they shout. If the temperature is 22 oC, how far away is the mountain that reflected the sound wave?
  4. At rest, a car's horn sounds the note A (440 Hz). The horn is sounded while the car is moving down the street. A bicyclist moving in the same direction with one-third the car's speed hears a frequency of 415 Hz. How fast is the car moving? Is the cyclist ahead of or behind the car?

Solutions