Wavelength, frequency, and speed of a Standing wave.

In summary, two oppositely traveling sinusoidal waves interfere to produce a standing wave with the wave function y=(1.50 m) sin(.400x) cos(200t), where x is in meters and t is in seconds. The wavelength is determined by the equation wavelength = 2*pi / k and has a value of 15.71 meters. The frequency is given by f = 2*pi / w and has a value of 31.83 Hz. The speed of the waves is calculated by multiplying wavelength and frequency, resulting in a value of 500 m/s. The letters k and w represent the wavenumber and angular frequency, respectively.
  • #1

Jenn_Lane2001

Hello,
Thank you all that helped me on the last problem. This other problem is also giving me a little problem.

Two sunusoidal waves travel in oppoiste directions interefere to produce a standing wave with the wave function.

y=(1.50 m) sin(.400x) cos(200t)

where x is in meters and t is in seconds. Determine the wavelength, frequency, and speed of the interfering waves.

Ok this is what I got...

Wavelength is =(velocity/frequency)
Frequnecy is = 1/time

now the problem i ran into is this is a simple plug in and find result problem however from the standing wave funtion what numbers go where. I can't seem to find it. Any help will be greatly appreciated.
Thank You

Jenn
 
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  • #2
Standing waves are given by

Y = 2A*sin(kx)*sin(wt) if that helps?

edit; k = n*pi/ L too, where L is the fundamental wavelength, you should have enough now.
 
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  • #3
ok so the wavefrequency is L = n*pi/k however what does n stand for and k. That is the problem I am having i am not sure what certian letters mean. Thank you for the help though.
 
  • #4
Ok a better one sorry is wavelength = 2*pi / k.

You probably know f = 2*pi / w, and c = f* wavelength.

Match that to the equation in my first reply and it should be straight forward.

K is the 'wavenumber' by the way. Try looking up standing waves in a textbook as well, it could help.
 
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  • #5
ok I think i got it now

Frequency's , since it's the same as the standing wave's:
F = 200 / 2pi = 31.83Hz.

Wavelength's is, since the wavelength of the sinusoids is the
same as the wavelength of the standing sin(0.4x) wave. That's
2pi / 0.4 = 15.71meters.
Finally, the speed of the waves is just wavelength x frequency = 15.71m x 31.83/s = 500m/s.

Does this look right and did i do it right?
 

1. What is a standing wave?

A standing wave is a type of wave that forms when two waves with the same wavelength and frequency travel in opposite directions and interfere with each other. This results in a wave pattern that appears to be standing still or not moving.

2. What is wavelength?

Wavelength is the distance between two consecutive peaks or troughs of a wave. It is measured in meters (m) or other units of length and is represented by the Greek letter lambda (λ).

3. What is frequency?

Frequency is the number of waves that pass a fixed point in a given amount of time. It is measured in hertz (Hz) or cycles per second and is represented by the symbol f.

4. How are wavelength, frequency, and speed of a standing wave related?

The speed of a standing wave is equal to the product of its wavelength and frequency. This means that as the frequency increases, the wavelength decreases, and vice versa. This relationship is described by the equation v = fλ, where v is the speed of the wave, f is the frequency, and λ is the wavelength.

5. What factors can affect the wavelength, frequency, and speed of a standing wave?

The wavelength, frequency, and speed of a standing wave can be affected by the medium through which it is traveling, the tension of the medium, and the length of the medium. Changes in these factors can result in changes to the properties of the standing wave.

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