Wave interference, boundaries, and superposition

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley

Wave interference, boundaries, and superposition

• Waves in motion from one boundary (the source) to another boundary (the endpoint) will travel and reflect.


Vertical applications of SHM

• As wave pulses travel, reflect, travel back, and repeat the whole cycle again, waves in phase will add and waves out of phase will cancel.


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.


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

Q15.9


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.

A15.9


Monster bass

You want to build a huge bass guitar with a 5m long bass string with a mass/length 0.04 kg/m and tune it to give a 20 Hz fundamental frequency (the lowest humans can hear).

• Calculate the tension of the string

• Calculate the frequency and wavelength of the second harmonic.


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.


The air in an organ pipe is replaced by helium (which has a faster speed of sound) 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.

Q16.4


The air in an organ pipe is replaced by helium (which has a faster speed of sound) 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.


A16.4


The air in an organ pipe is replaced by helium (which has a faster speed of sound) at the same temperature. How does this affect the normal-mode frequencies of the pipe?

A. The normal-mode frequencies are unaffected.

B. The normal-mode frequencies increase.

C. The normal-mode frequencies decrease.


Q16.5


The air in an organ pipe is replaced by helium (which has a faster speed of sound) at the same temperature. How does this affect the normal-mode frequencies of the pipe?

A. The normal-mode frequencies are unaffected.

B. The normal-mode frequencies increase.

C. The normal-mode frequencies decrease.


A16.5


Cross-sectional views reveal harmonic waves II


Cross-sectional views reveal harmonic waves III


A. 110 Hz.

B. 220 Hz.

C. 440 Hz.

D. 880 Hz.

E. 1760 Hz.

Q16.6

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


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.

A16.6


• Which mode (value of m) standing wave is this? At what frequency does the wave oscillate?

• Are the air molecules vibrating vertically or horizontally?

• At what distances from the left end of the tube do the molecules oscillate with max amplitude?

• Now the right end is covered. Redraw a standing wave in this case and answer the above questions.

Standing waves

0.77 m


Different instruments give the same pitch different “flavor”

• 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.


Wave interference … destructive or constructive


Two loud speakers are producing sound at 344 Hz and wavelength = 1 m. A microphone is placed such that the distance from loudspeaker 1, d1 = 2 m away and the distance from loudspeaker 2, d2 = 3 m away. The sound measured at the microphone

A. constructively interferes

B. destructively interferes

C. neither constructively nor destructively interferes

Interference


Two loud speakers are producing sound at 344 Hz and wavelength = 1 m. A microphone is placed such that the distance from loudspeaker 1, d1 = 2 m away and the distance from loudspeaker 2, d2 = 3 m away. The sound measured at the microphone




Interference


With the same sound playing, the microphone is moved such that the distance from loudspeaker 1, d1 = 2.5 m away and the distance from loudspeaker 2, d2 = 3.5 m away. The sound measured at the microphone




Interference


With the same sound playing, the microphone is moved such that the distance from loudspeaker 1, d1 = 2.5 m away and the distance from loudspeaker 2, d2 = 3.5 m away. The sound measured at the microphone




Interference


Sound interference

• For which sound frequencies does the microphone record constructive interference? Assume the sound coming out of the speakers is in phase.

• At the lowest frequency with constructive interference, how many wavelengths away is the microphone from speaker A and from speaker B?

• Destructive interference?


Soap bubble

You want to make a soap bubble that will primarily reflect red light (700 nm wavelength in vacuum).

How thick should the bubble be? Index of refraction of soapy water n = 1.33.

Is there more than one thickness that would work?

How could you reflect blue light? (no numbers, just explain)


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.

Q16.7


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.

A16.7

Wave interference, boundaries, and superposition

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