# Lecture in Vibrations and Waves | Giancoli Physics

(Last Updated On: March 21, 2020)

### Lesson Objectives – the students should be able to:

• State the conditions required to produce Simple Harmonic Motion (SHM).
• Determine the period of motion of an object of mass m attached to a spring of force constant k.
• Calculate the velocity, acceleration, potential, and kinetic energy at any point in the motion of an object undergoing SHM.
• Write equations for displacement, velocity, and acceleration as sinusoidal functions of time for an object undergoing SHM if the amplitude and angular velocity of the motion are known. Use these equations to determine the displacement, velocity, and acceleration at a particular moment of time.
• Determine the period of a simple pendulum of length L.
• State the conditions necessary for resonance. Give examples of instances where resonance is a) beneficial and b) destructive. Explain how damped harmonic motion can be achieved to prevent destructive resonance.
• Distinguish between a longitudinal wave and a transverse wave and give examples of each type of wave.
• Calculate the speed of longitudinal waves through liquids and solids and the speed of transverse waves in ropes and strings.
• Calculate the energy transmitted by a wave, the power of a wave and the intensity of a wave, across a unit area A.
• Describe wave reflection from a barrier, refraction as the wave travels from one medium into another, constructive and destructive interference as waves overlap, and diffraction of waves as they pass around an obstacle.
• Explain how a standing wave can be produced in a string or rope and calculate the harmonic frequencies needed to produce standing waves in string instruments.

### Summary of Chapter 11

• For SHM, the restoring force is proportional to the displacement.
• The period is the time required for one cycle, and the frequency is the number of cycles per second.
• Period for a mass on a spring:
• SHM is sinusoidal.
• During SHM, the total energy is continually changing from kinetic to potential and back.
• A simple pendulum approximates SHM if its amplitude is not large. Its period in that case is:
• When friction is present, the motion is damped.
• If an oscillating force is applied to a SHO, its amplitude depends on how close to the natural frequency the driving frequency is. If it is close, the amplitude becomes quite large. This is called resonance.
• Vibrating objects are sources of waves, which may be either a pulse or continuous.
• Wavelength: distance between successive crests.
• Frequency: number of crests that pass a given point per unit time.
• Amplitude: maximum height of crest.
• Wave velocity:
• Transverse wave: oscillations perpendicular to direction of wave motion.
• Longitudinal wave: oscillations parallel to direction of wave motion.
• Intensity: energy per unit time crossing unit area (W/m2):
• Angle of reflection is equal to angle of incidence.
• When two waves pass through the same region of space, they interfere. Interference may be either constructive or destructive.
• Standing waves can be produced on a string with both ends fixed. The waves that persist are at the resonant frequencies.
• Nodes occur where there is no motion; antinodes where the amplitude is maximum.
• Waves refract when entering a medium of different wave speed, and diffract around obstacles.
• A full mathematical description of the wave describes the displacement of any point as a function of both distance and time:

### Units of Chapter 11 – Keywords

• Simple Harmonic Motion
• Energy in the Simple Harmonic Oscillator
• The Period and Sinusoidal Nature of SHM
• The Simple Pendulum
• Damped Harmonic Motion
• Forced Vibrations; Resonance
• Wave Motion
• Types of Waves: Transverse and Longitudinal
• Energy Transported by Waves
• Intensity Related to Amplitude and Frequency
• Reflection and Transmission of Waves
• Interference; Principle of Superposition
• Standing Waves; Resonance
• Refraction
• Diffraction
• Mathematical Representation of a Traveling Wave