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Nodes of a Standing Wave (Cosine)
Learning Goal: To understand the concept of nodes of a standing wave.
The nodes of a standing wave are points where 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 standing wave, where represents the transverse displacement of a string that extends along the x direction. Here is a common mathematical form for such a wave:

where is the maximum transverse displacement of the string (the amplitude of the wave), which is assumed to be nonzero, is the wavenumber, is the angular frequency of the wave, and is time.

Part A
Which one of the following statements about wave is correct?
Which one of the following statements about wave is correct?

This wave is traveling toward

This wave is traveling toward .

This wave is oscillating but not traveling.

This wave is traveling but not oscillating.

Part B
At time , what is the displacement of the string ?
Express your answer in terms of , , and other previously introduced quantities.

= __________________

Part C
What is the displacement of the string as a function of at time , where is the period of oscillation of the string?
Express the displacement in terms of , , and only. That is, evaluate and substitute it in the equation for .

= __________________

Part D
At which three points , , and closest to but with will the displacement of the string be zero for all times? These are the first three nodal points.
Express the first three nonzero nodal points as multiples of the wavelength , using constants like . List the factors that multiply in increasing order, separated by commas.

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

1. An ocean wave travels 10.8 m in 6.9 s. The distance between two consecutive wave crests is 4.3 m. What is the frequency of the wave? Answer in units of Hz
2. Water waves in a lake travel 4.73 m in 1.01 s. The period of oscillation is1s.
What is the speed of the water waves? What is their wavelength
3. If you slosh the wate

See attached file for the graph.
A certain wave and its reflection simultaneously travel along a wire. The two waves are:
y1= .15 sin (5x - 3 Pi t) and y2= .15 sin (5x + 3 Pi t). When they combine, they form a standingwave.
PART a. Write the equation of the standingwave produced on the wire.
PART b. Calculate the dis

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

(See attached file for full problem description)
On quiz 2 below please explain 1-5 better and 7 - 10 better, specifically, what equations are used to solve each question, how are the numbers and equations worked out to see better. Please do the same for quiz 3 for problems 1-7.
See everything below this page and the n

A sound source sends a sinusoidal sound wave of angular frequency 3000 rad / s and amplitude 12.0 nm through a tube of air. The internal radius of the tube is 2.00 cm. (a) What is the average rate at which mechanical energy is transported to the opposite end of the tube? If an identical wave and the original wave travel alon

(See attached file for full problem description and figures)
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21.8
The figure shows a standingwave oscillating at 100 Hz on a string.
Part A : What is the wave speed?
21.5
A 40-cm-long tube has a 40-cm-long insert that can be pulled in and out. A vibrating tuning fork is held next to the tube. As the ins

Please do questions 1-5. Going through this lab, please see data table in second attachment, stringlab2.doc, when tried to solve for V th and the rest everything went wrong. V th never even was close to V average. This is throwing everything off. All data is assumed to be correct, but again V th is off. If cannot read here

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