C o n c e p t C h e c k If the length of a pendulum is doubled, what is the ratio of the new period to the old one? a. 2 b. 4 c. 1/2 d.  2

R e s o n a n c e & I n t e r f e r e n c e W h e n w a v e s c o m b i n e

R e s o n a n c e a n d D a m p i n g If the source of a periodic force matches the natural frequency of an oscillating object, it will oscillate at a higher amplitude. If the source does not match the natural frequency, damping occurs.

N a t u r a l F r e q u e n c y The frequency at which a system tends to oscillate is called its natural frequency.

N a t u r a l F r e q u e n c y How are string instruments designed to account for these two effects? What is different about each string? What does tuning do?

N a t u r a l F r e q u e n c y

R e s o n a n c e Resonance occurs when the periodic force is applied at the natural frequency. The energy of the resonant system increases with each application of the periodic force

C o n c e p t C h e c k Which is not an example of resonance? A.a person pushing a child higher and higher on a swing B.a child bouncing a ball up and down C.a singer singing a specific note, causing a glass to vibrate and break D.a trumpet player vibrating his lips to play a note

T a c o m a B r i d g e D i s a s t e r

R e s o n a n c e

I n t e r f e r e n c e Constructive interference occurs when two waves add upon eachother to create a wave with an additive amplitude. The forces acting on a given particle are in the same direction Destructive interference occurs when one wave has a positive amplitude and another has a negative amplitude. Some of the forces acting on individual particles cancel out.

I n t e r f e r e n c e

P r a c t i c e A P P r o b l e m 1 Wave pulses travel toward each other along a string as shown below. Answer the following questions in terms of the resulting superposition of the pulses when their centers are aligned. (A) Rank the maximum amplitude of the resulting superposition from smallest to largest. (B) Rank the magnitude of the maximum amplitude of the resulting superposition from smallest to largest.

P r a c t i c e A P P r o b l e m 2 Sound waves are traveling through air when they encounter a steel barrier. Some of the sound waves are reflected and inverted, while the rest are transmitted through the steel barrier. The restoring forces within the steel are significantly higher than that of air. Which of the following changes occur to the sound waves at the air/steel boundary? Select two answers. A.their amplitude decreases in the steel because some of the waves are reflected. B.their speed increases in the steel because the restoring forces are higher. C.their frequency decreases in the air because the restoring forces are lower. D.their wavelength decreases in the air because the reflected waves are inverted