Chapter 14 Notes Vibrations and Waves

Section 14.1 Objectives Use Hooke’s law to calculate the force exerted by a spring. Calculate potential energy of an elastic spring. Identify objects in simple harmonic motion. Determine variables that affect the period of a pendulum. Describe the affect of resonance on an object.

Periodic Motion Examples – clock pendulum, vibrating guitar string

Simple Harmonic Motion Described by two quantities: – Period – Amplitude

Hooke’s Law

Potential Energy in a Spring

Example Problem A spring stretches by 18 cm when a bag of potatoes weighing 56 N is suspended from its end. a.Determine the spring constant. b.How much elastic potential energy is stored in the spring when it is stretched this far?

Pendulums

Example Problem How long must a pendulum be on the Moon, where g=1.6 m/s 2, to have a period of 2.0 s?

Resonance

Section 14.2 Objectives Differentiate between transverse and longitudinal waves. Determine wave speed, wavelength, and frequency using corresponding equations.

Mechanical Waves Types – Transverse – Longitudinal – Surface

Transverse Waves

Longitudinal Waves

Surface Waves

Measuring a Wave Speed Amplitude Wavelength Phase Period Frequency

Example Problem A sound wave has a frequency of 192 Hz and travels the length of a football field, 91.4 m, in s. a)What is the speed of the wave? b)What is the wavelength of the wave? c)What is the period of the wave? d)If the frequency was changed to 442 Hz, what would be the new wavelength and period?

Section 14.3 Objectives Relate a wave’s speed to the medium in which the wave travels. Describe the motion of a wave as it encounters boundaries. Apply the principle of superposition to wave interference.

Waves at Boundaries

Free boundary – waves/free.cfm waves/free.cfm Fixed boundary – waves/fix.cfm waves/fix.cfm

Superposition of Waves Interference – Constructive – Destructive waves/U10L3c.cfm waves/U10L3c.cfm

Standing Waves