Standing Waves PHYS116 A01 111214 Lecture 36 Momchil

Standing Waves PHYS-116 A-01, 11/12/14, Lecture 36 Momchil Velkovsky

Wave Superposition, Boundary Conditions

Standing waves on a string Fixed at both ends, the resonator was have waveforms that match. In this case, the standing waveform must have nodes at both ends. Differences arise only from increased energy in the waveform.

Complex standing waves • As the shape and composition of the resonator change, the standing wave changes also. Regard Figure 1, a multidimensional standing wave. Figure 2 provides many such multidimensional shapes.

While a guitar string is vibrating, you gently touch the midpoint of the string to ensure that the string does not vibrate at that point. The lowest-frequency standing wave that could be present on the string A. vibrates at the fundamental frequency. B. vibrates at twice the fundamental frequency. C. vibrates at three times the fundamental frequency. D. vibrates at four times the fundamental frequency. E. not enough information given to decide

A problem

Longitudinal waves show the sinusoidal pattern A motion like the pulses of a speaker cone will create compressions and rarefactions in a medium like air. After the pulse patterns are seen, a sinusoidal pattern may be traced.

Sound waves may be graphed several ways

Speed of sound in liquids and solids 1240 km/h, 770 mi/h • The speed of sound will increase with the density of the material.

Standing sound waves and normal modes • Experiments often done in a first physics course laboratory will use common materials to reveal standing sound waves in resonance.

Cross-sectional views help us visualize the wave Nodes and antinodes will line up so that nodes are found where the resonator is closed antinodes at an open pipe. The crosssectional view helps to see the pattern.

Cross-sectional views reveal harmonic waves II

Cross-sectional views reveal harmonic waves III

Different instruments give the same pitch different “favor” The same frequency, say middle c at 256 Hz, played on a piano, on a trumpet, on a clarinet, on a tuba … they will all be the same pitch but they will all sound different to the listener.

The speed of sound can be revealed by a resonant pipe • The frequency, speed of sound, and wavelength are all used to measure normal modes in a pipe

Sound intensity • Go beyond the wave on a string and visualize, say … a sound wave spreading from a speaker. That wave has intensity dropping as 1/r 2. . b= (10 d. B)log(I/I 0), I 0=10 -12 W/m

The logarithmic decibel scale of loudness Table 16. 2 shows examples for common sounds.

Wave interference … destructive or constructive

Sounds playing on a speaker system can interfere vs=350 m/s at what frequencies do constructive and destructive interference occur?

Slightly mismatched frequencies cause audible “beats”

Reading for next time • Chapter 17