Vibrations and Waves: Physics Problems and Solutions

Posted on Feb 19, 2025 in Physics

Vibrations & Waves

1. 1) A wiggle in time is a:

   1. vibration.
   2. wave.
   3. both
   4. neither

   Answer: a

2. 2) A common source of wave motion is a:

   1. wave pattern.
   2. harmonic object.
   3. vibrating object.
   4. region of variable high & low pressure.
   5. none of these

   Answer: c

3. 3) Like a transverse wave, a longitudinal wave has:

   1. amplitude, frequency, wavelength, & speed.
   2. amplitude, frequency, & wavelength.
   3. amplitude, wavelength, & speed.
   4. wavelength, speed, & frequency.
   5. amplitude, frequency, & speed.

   Answer: a

4. 4) How many vibrations per second are associated with a 101-MHz radio wave?

   1. less than 101,000,000
   2. 101,000,000
   3. more than 101,000,000

   Answer: b

5. 5) When a pendulum clock at sea level is taken to the top of a high mountain, it will:

   1. gain time.
   2. lose time.
   3. neither gain nor lose time.

   Answer: b (@ high altitudes, the acceleration due to gravity will decrease, decreasing the pull of gravity on the pendulum. Thus, it would have a longer period, & because the frequency is the inverse of the period, it will have a smaller frequency.)

6. 6) If you double the frequency of a vibrating object, its period:

   1. doubles.
   2. halves.
   3. is quartered.

   Answer: b (period & frequency are reciprocals or inverses of each other.)

7. 7) If at a concert you run toward the orchestra, the frequency of the sound you hear will be:

   1. decreased.
   2. increased.
   3. neither decreased nor increased.

   Answer: b (like a train horn coming at you gets higher in pitch because of the Doppler effect.)

8. 8) A pendulum of mass 2.0 kg is raised to a height of 0.4 m above the lowest point in its swing & then is released from rest. If air resistance can be ignored, how high will the pendulum swing on the other side of its motion?

   1. half as high
   2. 1/4 as high
   3. 1/3 as high
   4. just as high
   5. not move

   Answer: d

   A pendulum swing is simple harmonic motion, so the pendulum is at rest at the extremes of its motion, & it possesses only potential energy at those positions. Thus, the potential energy at each extreme must be the same. The potential energy of a pendulum depends only upon the height of the pendulum above the lowest point, so the 2 heights must be the same. Thus, the answer is 0.4 m.

   
   

9. 9) For the pendulum in the previous problem, how fast will it move at the lowest point in its swing?

   1. 0.5 m/s
   2. 1 m/s
   3. 5 m/s
   4. 10 m/s
   5. none of these

   Answer: e

   This problem can be solved using the principle of conservation of mechanical energy in exactly the same manner as we solved problem # 6 & problem # 8. Thus, we have:

   pe₁ + ke₁ = pe₂ + ke₂

   mgh₁ + 0 = 0 + 1/2 m(v₂)²

   gh₁ = 1/2 (v₂)²

   (9.8 m/s²) (0.4 m) = (1/2) (v₂)²

   (v₂)² = 7.84 m²/s²

   v₂ = 2.8 m/s

10. 10) A spring of spring constant 60 N/m is stretched a distance of 0.3 m from its equilibrium position. Calculate the increase in the potential energy of the spring.

    1. 45 joules
    2. 9 joules
    3. 8 joules
    4. 2.0 joules
    5. none of these

    Answer: e

    The potential energy of a spring is given by:

    pe_s = 1/2 kx²

    pe_s = (1/2) (60 N/m) (0.3 m)²

    pe_s = 2.7 N m = 2.7 J

Group Question

1. 1) Titania is the largest moon of the planet Uranus. It is 1/8 the radius of Earth & 1/1700 the mass of Earth.

   1. What is the acceleration due to gravity at the surface of Titania?
   2. What is the average density of Titania? (This density is smaller than the density of rock found on Earth & so leads us to believe Titania is composed of ice.)

   Answer: From the force of gravity on an object effected by Earth we have:

   

   & where near the Earth the gravitational acceleration reduces to:

   

   In a like manner the acceleration due to gravity at the surface of Titania is given by:

   

   & so the acceleration on Titania (mt mass titanium, rt the radius of titanium)