Understanding Vibrations and Waves: Solved Physics Examples
Vibrations and Waves
1) A wiggle in time is a:
A) vibration.
B) wave.
C) both
D) neither
Answer: A
2) A common source of wave motion is a:
A) wave pattern.
B) harmonic object.
C) vibrating object.
D) region of variable high and low pressure.
E) none of these
Answer: C
3) Like a transverse wave, a longitudinal wave has:
A) amplitude, frequency, wavelength, and speed.
B) amplitude, frequency, and wavelength.
C) amplitude, wavelength, and speed.
D) wavelength, speed, and frequency.
E) amplitude, frequency, and speed.
Answer: A
4) How many vibrations per second are associated with a 101-MHz radio wave?
A) less than 101,000,000
B) 101,000,000
C) more than 101,000,000
Answer: B
5) When a pendulum clock at sea level is taken to the top of a high mountain, it will
A) gain time.
B) lose time.
C) neither gain nor lose time.
Answer: B (At high altitudes, the acceleration due to gravity will decrease, decreasing the pull of gravity on the pendulum. Thus it would have a longer period, and because the frequency is the inverse of the period, it will have a smaller frequency.
6) If you double the frequency of a vibrating object, its period:
A) doubles.
B) halves.
C) is quartered.
Answer: B (Period and frequency are reciprocals or inverses of each other.)
7) If at a concert you run toward the orchestra, the frequency of the sound you hear will be:
A) decreased.
B) increased.
C) neither decreased nor increased.
Answer: B (Like a train horn coming at you gets higher in pitch because of the Doppler effect.)
8) A pendulum of mass 2.0 kg is raised to a height of 0.4 m above the lowest point in its swing and then is released from rest. If air resistance can be ignored, how high will the pendulum swing on the other side of its motion?
A) Half as high
B) One fourth as high
C) One third as high
D) Just as high
E) Not move
Answer D
A pendulum swing is simple harmonic motion, so the pendulum is at rest at the extremes of its motion, and 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 two heights must be the same. Thus the answer is 0.4 m.
9) For the pendulum in the previous problem, how fast will it move at the lowest point in its swing?
A) 0.5 m/s
B) 1 m/s
C) 5m/s
D) 10 m/s
E) 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 number 6 and problem number 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
Q10) 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.
- 45 joules
B) 9 joules
C) 8 joules
D) 2.0 joules
E) none of these
Answer E
The potential energy of a spring is given by
PEs = 1/2 kx2
PEs = (1/2) (60 N/m) (0.3 m)2
PEs = 2.7 N m = 2.7 J