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Standing wave problems

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1. Suppose that there was a ride at an amusement park which was titled "The Standing Wave." Which location - node or antinode - on the ride would give the greatest thrill?

2. A standing wave is formed when
a. a wave refracts due to changes in the properties of the medium.
b. a wave reflects off a canyon wall and is heard shortly after it is formed.
c. red, orange, and yellow wavelengths bend around suspended atmospheric particles.
d. two identical waves moving different directions along the same medium interfere.

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Solution Preview

1. The node doesn't move. The antinode is continually vibrating from a high to a low displacement - perfect for thrill ...

Solution Summary

Standing node and antinode properties. Standing wave properties.

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resonance in longitudinal waves and wave problem

The bottle is acting as a Helmholtz resonator. This is the same phenomenon that acts when you blow across the top of the bottle. The volume of the air inside the bottle and the mass of air in the neck of the bottle work together to determine the pitch of the resulting sound. As the bottle fills, the volume of air decreases, and the pitch increases.

To understand Helmholtz resonance, lets first about resonance in general. An example of resonance is seen when you attach a mass to a spring and shake that spring with you hand In the case of a mass attached to a spring, its easy to visualize. You can shake the spring at whatever frequency you want, but there is a particular frequency where you don't need to shake your hand very much to get a large amplitude response. That's resonance.

In Helmholtz resonance, the "mass" is the amount of air inside the neck of your bottle. The "spring" is the volume of air inside your bottle - as you fill the bottle with water, you're changing the volume of air inside the bottle. There is an inverse relationship between the resonant frequency and the volume inside the bottle. SO as the volume decreases the pitch goes up.

And so you hear a tone rising in pitch as the bottle fills.

See attached for the rest.

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