standing wave question?

Question

Fill in the values in the chart for the first four standing waves supported on a string fixed at both ends:

it asks for Number of antinodes, number of nodes, wavelength, frequency, and velocity.

i have no idea what exactly i am supposed to do...

do you guys have any ideas?

Answer 1

Nodes are places that have zero amplitude.
Antinodes have maximum amplitude.
Wavelength is twice the distance between successive nodes.

Velocity = frequency * wavelength

Check this out for some help...
http://www.physicsclassroom.com/Class/waves/u10l4c.html

Answer 2

l = vt = v(1/f); where l = wavelength, v = velocity of the wave, t = period (the time it takes to travel one wavelength), and f = 1/t = the frequency of that wave (where frequency is the number of times the wave oscillates one full cycle in that period of time t).

A node is a point along a standing wave where the wave has minimal amplitude (usually at some average value around which the wave oscillates) [See source.] The distance between nodes is 1/2 l, one-half the wavelength, for the simple sine wave.

An anti node is where the transverse wave does its major oscilliations; so that's where the wave will move up and down most. Thus, the amplitudes at the anti nodes can reach the absolute maximums relative to the average.

To get a standing wave from a taut string of length L, the length of the wave (l) must be some whole number fraction of the length of the string. That is l = L/n; where n is a whole number. In the source example, n = 2; so that l = L/2 which means the "string" in the example is two wave lengths long.

Thus, if we were to shorten L, the wave length l would need to shorten as well to support a standing wave. And from l = vt; where l/t = v = lf, as the l shortens the frequency has to go higher for a constant speed of sound (v = constant). Thus, the higher tones on a piano come from the short strings and the lower ones come from the longer strings.

Answer 3

Antinodes are the places in the standing wave where it oscillates between pos and neg amplitude.
Nodes are the places where they do not move at all.
(The most basic standing wave has two nodes and one antinode)
Wavelength is just the distance between nodes (i think, or maybe its twice that distance)
Frequency = (number of segments/2) * (Velocity / length of a segment) (I think). If you know the period (time it takes for one vibration) then freq = 1/period.
velocity = wavelength/period (or wavelength * frequency)

Answer 4

the first antinode corresponds to the mandatory frequency. The allowed wavelenghts of the wave is given by technique of 2L/n, the position Lis the lenght of the string and n is the mode(or the style of antinodes required, in case you want). you will get this expression by technique of putting out with the overall expression for a wave, sin(wt-kx), w is the angular frequency. Now the pondered wave travels contained in the option route and is shifted by technique of slightly of one hundred eighty ranges. So the pondered wave is sin(kx+wt). the resultant wave is the sum of both waves. Now thinking the string is tied on both ends, we get 2sinkxcoswt=0 at x=L.SO sinkL=0, which elements lambda=2L/n (this expression is valid for all circumstances, ok=2pi/(lambda)). ans)0.4 Hz b)0.8 Hz c)a million.6 Hz