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Reaading wave graphs (1 Viewer)
- Thread starter munkaii
- Start date
Think of it as the oscillations of a point of the medium that is carrying the longitudinal wave. Observe this picture:
If you take any individual point on the spring you will find that it oscillates back and forth when the longitudinal wave passes through it. Your graph is showing the oscillations of one of these points over time.
Is there any information you're trying to get from the graph like f or λ?
If you take any individual point on the spring you will find that it oscillates back and forth when the longitudinal wave passes through it. Your graph is showing the oscillations of one of these points over time.
Is there any information you're trying to get from the graph like f or λ?
AntiHyper
Revered Member
KFunk: how did u get the lambda sign?
wavelength
The distance between one peak or crest of a wave of light, heat, or other energy and the next corresponding peak or crest.
With pressure waves, it's the most positively displaced particle to the nect corresponding positively displaced particle.
wavelength
The distance between one peak or crest of a wave of light, heat, or other energy and the next corresponding peak or crest.
With pressure waves, it's the most positively displaced particle to the nect corresponding positively displaced particle.
Will Hunting
Member
Hey man,
Displacement vs. Time Graphs:
There isn't much to this. The only questions that may arise on this topic will involve calculations of average and instantaneous velocity, or calculations of total distance covered over a given interval of time.
For instantaneous velocity, the gradient of an interval joining any two points on the graph will give the instantaneous velocity for any point lying on that interval (including the endpoints themselves). Find the gradient using rise/run (displacement/time).
For average velocity, average the gradients of all linear intervals you see on the graph (what I mean by this is find the gradient of each part of the zig-zag, add them all up and take their average). Any curve on the graph indicates an acceleration and, hence, makes average velocity impossible to determine by this method. Note that negative gradients indicate negative velocities (velocity is a vector).
Use a vector addition to find total distance covered over a given interval of time, accounting for places where displacement is negative.
KFunk mentions tracing the motion of one point in the medium, however, it must be remembered that a longitudinal wave is a series of vibrations experienced by all particles transferring the wave's energy (a longitudinal wave requires a mechanical medium through which to travel, unlike transverse waves). Applying this to your dot diagram, the distance between the place where the dots are just beginning to compress to the place where they are the most condensed (or between the place where the are just beginning to spread thin to the place where they occur most sparsely) is the amplitude of your wave. The distance between adjacent places of highest (or lowest) density is the wavelength of your wave.
Solve the universal wave equation, f = v/λ for frequency. Alternatively, if time is on the horizontal axis, measure the number of waves, and/or fractions thereof occuring in a one second frame and express in units of waves/sec, or Hz.
No spaces.
Displacement vs. Time Graphs:
There isn't much to this. The only questions that may arise on this topic will involve calculations of average and instantaneous velocity, or calculations of total distance covered over a given interval of time.
For instantaneous velocity, the gradient of an interval joining any two points on the graph will give the instantaneous velocity for any point lying on that interval (including the endpoints themselves). Find the gradient using rise/run (displacement/time).
For average velocity, average the gradients of all linear intervals you see on the graph (what I mean by this is find the gradient of each part of the zig-zag, add them all up and take their average). Any curve on the graph indicates an acceleration and, hence, makes average velocity impossible to determine by this method. Note that negative gradients indicate negative velocities (velocity is a vector).
Use a vector addition to find total distance covered over a given interval of time, accounting for places where displacement is negative.
If you're more comfortable with the transverse waveform, you can convert the dot diagram into a sine curve. You do this by noting that transverse and longitudinal waves have equivalent characteristics. A compression corresponds to a peak and a rarefaction to a trough on a sine curve (I say sine curve because it's the simplest waveform to work with when trying to understand this concept. In actuality, transverse waveforms would usually be jagged and irregular in shape).KFunk said:Think of it as the oscillations of a point of the medium that is carrying the longitudinal wave. Observe this picture:
If you take any individual point on the spring you will find that it oscillates back and forth when the longitudinal wave passes through it. Your graph is showing the oscillations of one of these points over time.
KFunk mentions tracing the motion of one point in the medium, however, it must be remembered that a longitudinal wave is a series of vibrations experienced by all particles transferring the wave's energy (a longitudinal wave requires a mechanical medium through which to travel, unlike transverse waves). Applying this to your dot diagram, the distance between the place where the dots are just beginning to compress to the place where they are the most condensed (or between the place where the are just beginning to spread thin to the place where they occur most sparsely) is the amplitude of your wave. The distance between adjacent places of highest (or lowest) density is the wavelength of your wave.
Graphically, λ is found as above (or more easily by converting to transverse)KFunk said:
Solve the universal wave equation, f = v/λ for frequency. Alternatively, if time is on the horizontal axis, measure the number of waves, and/or fractions thereof occuring in a one second frame and express in units of waves/sec, or Hz.
No probs, man. Just type &, then lambda, then ;AntiHyper said:
No spaces.
Last edited:
http://www.boredofstudies.org/community/showthread.php?t=7127&page=3AntiHyper said:
That thing is my bible for notation on this board (thanks Xayma!). You can get any greek character by typing &(name); . It's pretty easy to get the greek letters because you don't need to remember any weird code or abreviation for them you just type α β γ δ Δ (btw, using a capital at the start puts the greek letter into its upper case form) ξ Φ θ etc...