Waves Sound and interference PHYS116 A02 4413 Lecture

Waves: Sound and interference PHYS-116 A-02, 4/4/13, Lecture 21 Momchil Velkovsky

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 reveal harmonic waves

When you blow air into an open organ pipe, it produces a sound with a fundamental frequency of 440 Hz. If you close one end of this pipe, the new fundamental frequency of the sound that emerges from the pipe is • • • A. 110 Hz. B. 220 Hz. C. 440 Hz. D. 880 Hz. E. 1760 Hz.

Cross-sectional views reveal harmonic waves III

The air in an organ pipe is replaced by helium (which has a lower molar mass than air) at the same temperature. How does this affect the normal-mode wavelengths of the pipe? • • A. The normal-mode wavelengths are unaffected. B. The normal-mode wavelengths increase. C. The normal-mode wavelengths decrease. D. The answer depends on whether the pipe is open or closed.

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.

The air in an organ pipe is replaced by helium (which has a lower molar mass than air) at the same temperature. How does this affect the normal-mode wavelengths of the pipe? • • A. The normal-mode wavelengths are unaffected. B. The normal-mode wavelengths increase. C. The normal-mode wavelengths decrease. D. The answer depends on whether the pipe is open or closed.

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

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”

You hear a sound with a frequency of 256 Hz. The amplitude of the sound increases and decreases periodically: it takes 2 seconds for the sound to go from loud to soft and back to loud. This sound can be thought of as a sum of two waves with frequencies • • • A. 256 Hz and 2 Hz. B. 254 Hz and 258 Hz. C. 255 Hz and 257 Hz. D. 255. 5 Hz and 256. 5 Hz. E. 255. 75 Hz and 256. 25 Hz.

The Doppler Effect —moving listener, moving source • As the object making the sound moves or as the listener moves (or as they both move), the velocity of sound is shifted enough to change the pitch perceptively.

On a day when there is no wind, you are moving toward a stationary source of sound waves. Compared to what you would hear if you were not moving, the sound that you hear has • • A. a higher frequency and a shorter wavelength. B. the same frequency and a shorter wavelength. C. a higher frequency and the same wavelength. D. the same frequency and the same wavelength.

On a day when there is no wind, you are at rest and a source of sound waves is moving toward you. Compared to what you would hear if the source were not moving, the sound that you hear has • • A. a higher frequency and a shorter wavelength. B. the same frequency and a shorter wavelength. C. a higher frequency and the same wavelength. D. the same frequency and the same wavelength.

Galaxies running away

Doppler effect problems The frequency of the whistle is 500 Hz, What is the frequency that the person on the ground hears? What is the frequency that a person in the train hears? What if there is wind?

Very fast aircraft can outrun the sound they generate • A “sonic boom” can be heard when an aircraft’s speed overcomes the sound it generates. • Before Chuck Yeager’s flight, designers were not sure the plane would survive.

Cherenkov Light