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Two waves simultaneously present on a long string have a phase difference between two waves is so that a standing wave formed from their combination is described by

   

 (a) Despite the presence of the phase angle , is it still true that the nodes are one-half wavelength apart?  

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Anil Kumar G.
Anil Kumar G.Lv10
8 Nov 2020

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Related textbook solutions

Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

Related questions

A string of length 2.50 m is fixed at both ends. When the stringvibrates at a frequency of 85.0 Hz, a standing wave with five loopsis formed.
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1) The equation of a transverse wave on a string is
y = (2.0mm) sin[(20 m-1)x - (600 s-1)t]

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2) What phase difference between two identical traveling waves,moving in the same direction along a streched string, results inthe vombined wave having an amplitude 1.50 times that of the commonamplitude of the two combining waves? Express your answer in (a)degress, (b) radians, and (c) wavelengths.

3) A rope, under a tension of 200 N and fixed at both ends,oscillates in a second-harmonic standing wave pattern. Thedisplacement of the rope is given by

y= (0.10 m (sin π/2) sin 12πt,

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A string of mass .03 kg and length 2 m is fixed at one end, anddriven with an oscillator at the other end. The oscillator inducestraveling waves on the string of the form
y=A sin (kx-(omega)t) which traveled down the string, hit the fixedend, and get reflected back as a wave with the form y=Asin(kx+(omega)t).
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So I have: m = 0.03 kg and L = 2 m
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(lambda) = 2L = 4 m
k = 2(pi)/(lambda) = (pi)/2
µ = m/L = 0.015 kg/m
,but all the equations I know to find velocity involve eithertension or frequency or another variable that I don't have. How doI find the velocity with what I'm given?

b.) I think that 4 nodes is the 2nd harmonic frequency (?) wheren=2 in the equation
f = n * (v/2L). Is this right? If so, I can easily find it when Ihave the answer for velocity.

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[sin a + sin ß = 2 sin ((a+ß)/2) cos ((a-ß)/2)]

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