A tube of air is open at only one end and has a length of 1.5 m. This tube sustains a standing wave at its third harmonic. What is the distance between one node and the adjacent antinode?

Solution Summary

This solution contains a diagram representing the harmonic motion of the air in the tube and contains step-by-step calculations to determine the distance between anode and an antinode.

SEE ATTACHMENT #1 for the general form of the equation of standingwaves.
A standingwave is set up in a guitar string. Find the first harmonic frequency. Then for a new frequency find new string tension and length.
A guitar string is .64 m long and has a linear density of .0004 kg/m. The tension is set at 55 newtons.

See attached file for full problem description.
9.2 Show that the standingwave f(z,t) = Asin(kz)cos(kvt) satisfies the wave equation, and express it as the sum of a wave travelling to the left and a wave traveling to the right as shown in the following equation:
F(z,t) = g(z -vt) + h(z + vt)

A water wave is called a deep-water wave if the water's depth is more than 1/4 of the wavelength. The speed of a deep water wave depends on its wavelength:
v = sqrt((g.lambda)/2pi).
Longer wavelengths travel faster. Let's apply to this to a standingwave. Consider a diving pool that is 5.0 m deep and 10.0 m wide. Standing w

The diagrams attached represent the polarization states of light. In each case the wave is traveling along the x-axis in the positive x direction.
i) Which diagram represents linear polarized light at 45 degrees?
ii) Which diagram represents left circular light? Explain.
iii) Which diagram represents un-polarized light?

Two pieces of steel wire with identical cross-sections have lengths of L and 2L. Each of the wires is fixed at both ends and stretched so that the tension in the longer wire is three times greater than that in the shorter wire. If the fundamental frequency in the shorter wire is 64.1 Hz, what is the frequency of the second harmo

A vibrating stretched string has length 38 cm, mass 25 grams and is under a tension of 30 newtons. What is the frequency to the nearest Hz of its 3rd harmonic?
If the source of the wave was an open organ pipe of the same length as the wire, what would be the frequency of the 2th harmonic?

The following are two harmonic oscillator wave functions:
S(x) = N exp(-max/2h)(2mwx/h)
S(x) = N exp(-max/2h)[8(mwx/h)^3 - 12mwx/h]
where N = .
Show that they are a) normalized, and b) orthogonal

The nodes of a standingwave are points at which the displacement of the wave is zero at all times. Nodes are important for matching boundary conditions, for example, that the point at which a string is tied to a support has zero displacement at all times (i.e., the point of attachment does not move).
Consider a standingwave

A guitar string is vibrating in its fundamental mode, with nodes at each end. The length of the segment of the string that is free to vibrate is 0.380 m. The maximum transverse acceleration of a point at the middle of the segment is 8800 m/s^2 and the maximum transverse velocity is 3.50 m/s.
a) What is the amplitude of this s