2.4 Problems

    Section 2.1
  1. Period and Frequency.
    a) What is the period of this wave?
    b) What is the frequency of this wave?
  2. Period and Frequency.
    a) What is the period of this wave?
    b) What is the frequency of this wave?
  3. Period and Frequency of a record player.
    Before CD’s people listened to records on a turntable. If the turntable revolved at 45 revolutions per minute, what is the period of this system in seconds? What is the frequency in Hz?

    4. Section 2.2
  4. Unit conversion:
    a) Convert 55 miles/hour to ft/sec:
    b) Convert 343 meters/sec to miles/hour:

    5. Section 2.3
  5. Maximum speed of your car.
    What does the maximum speed of your car depend on?
  6. String waves.
    The frequency of the fundamental of a string is given by the formula:
    .
    a) If I increase the length, will the frequency increase or decrease?
    b) If I increase the tension, will the frequency increase or decrease?
    c) If I increase the string density, U, will the frequency increase or decrease?
    d) If I change the length by a factor of 5, by what factor does the frequency change?
    e) If I change the tension by a factor of 5, by what factor does the frequency change?
    f) If I change the string density by a factor of 5, by what factor does the frequency change?
  7. Frequency of a Vibrating String.
    Refer to the formula for a vibrating string in Section 2.2.
    a) If you increase the density, U, of a string, the frequency will (increase | decrease | stay the same)?
    b) What has a greater effect on the frequency of the string: Doubling the density or doubling the length?
    c) Originally, the string has a frequency of 375 Hz. If I increase the tension by a factor of 2.4, what is the new frequency of the string?
  8. String Dependencies.
    Refer to the formula for a vibrating string in Section 2.2.
    a) If I double the length of the string, will the frequency increase or decrease and by what factor?
    b) If I decrease the density of the string by a factor of 16, will the frequency increase or decrease and by what factor?
    c) If I increase the tension by a factor of 4, will the frequency increase or decrease and by what factor?
    d) If I increase the tension by a factor of 3, by what factor should I change the density to keep the frequency the same?
    e) If I decrease the density by a factor of 4, by what factor should I change the length to keep the frequency the same?
  9. String waves.
    The frequency of the fundamental of a string is given by the formula:
    .
    I start with a frequency of 700 Hz. If I increase the tension by a factor of 4 and increase the density of the string by a factor of 9, what will be the new frequency?
  10. Dependencies.
    The frequency of the fundamental of a string is given by the formula:
    ,
    where L is the length of the string, T is the tension and U in the density.

    a) If I double the length of the string, how will the frequency change?
    b) If I increase the density of the string by a factor of 16, how will the frequency change?
    c) If I increase the tension by a factor of 9, how will the frequency change?
    d) If I increase the tension by a factor of 3, how should I change the density to keep the frequency the same?
    e) If I increase the density by a factor of 4, how should I change the length to keep the frequency the same?
  11. Orbits of the Planets.
    The period of the orbit of a planet around the sun is proportional to
    .
    R is the distance from the Sun and Msun is the mass of the Sun.

    a) If I decrease the distance, will the period increase or decrease?
    b) If I increase the mass, will the period increase or decrease?
    c) If I change the distance by a factor of 5, by what factor does the period change?
    d) If I change the mass by a factor of 5, by what factor does the period change?
  12. Orbits.
    The period of the orbit of a planet around the sun is proportional to
    .
    R is the distance from the Sun and Msun is the mass of the Sun.

    a) If the Earth was twice its distance from the Sun how long would it take the Earth to circle the Sun?
    b) If the Sun was three times as massive, how long would it take the Earth to circle the Sun?
  13. Wave Velocity.
    The speed of a wave on a string is
    ,
    where M is the mass on the end of the string, g is the acceleration of gravity and U is the mass per unit length of the string. For a particular string, a mass of 1 kg gives a velocity of 100 m/sec. What mass would produce a velocity of 300 m/sec?
  14. Helium versus Air.
    The density of helium is 7 times smaller than air. For any gas, the speed of sound is given by:
    .
    If the pressure is kept the same, what is the speed of sound in helium?
  15. Xenon versus Air.
    The density of helium is 4.7 times larger than air. For any gas, the speed of sound is given by:
    .
    If the pressure is kept the same, what is the speed of sound in xenon?
  16. Guitar strings.
    The speed of a wave on a string is given by:
    .
    A particular string gives a speed of 400 m/sec. If we want to increase the speed to 600 m/sec, by what factor should we change the density of the string, if we keep the tension the same?
  17. Speed of sound.
    The speed of sound depends on the air pressure and the air density in the following way:
    .
    We can change the density of air by changing its composition.

    a) In normal air the speed of sound is 343 m/sec. If I increase the density of the air by a factor of 3, does the speed of sound increase or decrease? By what factor will it increase or decrease?
    b) If I want to increase the speed by a factor of 4.5, how should I change the density of the air?
  18. Pendulum Clock
    Determine how the frequency, f, of a pendulum clock depends on the length, L, of the pendulum using the following data:
    19.

     

    Length, L

    Frequency, f

    L*f

    f/L

    1

    0.1 meter

    1.576 Hz

     

     

     

    2

    0.3 meter

    0.910 Hz

     

     

     

    3

    0.8 meter

    0.557 Hz

     

     

     

    4

    1.2 meter

    0.455 Hz

     

     

     

    5

    1.9 meter

    0.361

     

     

     
  19. Graphs.
    a) Graph the functions f(x) = cos(x) and g(x) = sin(x), measure x in radians:

    b) Graph the functions h(x) = x2/10 and k(x) =

.