The equation of a transverse wave traveling along a very long string is y=6\s

actever6a

actever6a

Answered question

2021-11-10

The equation of a transverse wave traveling along a very long string is y=6sin(0.02πx+4πt), where x and y are expressed in centimeters and t is in seconds. Determine (a) the amplitude, (b) the wavelength, (c) the frequency, (d) the speed, (e) the direction of propagation of the wave, and (f) the maximum transverse speed of a particle in the string. (g) What is the transverse displacement at x = 3.5 cm when t = 0.26 s?

Answer & Explanation

Pulad1971

Pulad1971

Beginner2021-11-11Added 22 answers

Step 1 
GIVEN: 
y=6sin(0.02πx+4πt) 
t=0.26sx=3.5cm 
By comparing the given eqution to the general wave function form 
y=ymsin(kxωt+φ) 
Step 2 
(a)Amplitude  ym=6cm 
Step3 
(b)k=2πλ=0.02π=2π0.01  Thereforeλ=100cm 
Step 4 
(c)ω=4π=2πf 
Therefore  f=2H 
Step 5 
(d)The speed of the wave  v=fλ=2×100=200cms 
Step 6 
(e) Since w in the given wave equation has a +ve sign, the direction of the wave's propagation is in the -ve direction of the x-axis.
Step 7 
(f)The maximum transverse speed  um=ω   ym=4π×6=24π=75.39cms 
Step 8 
(g)Substituting In the given equation witht=0.26s   x=3.5cm 
y=6sin(0.02π×3.5+4π×0.26) 
Thus,
y=-2cm 
Step9 
(a)ym=6cm 
(b)λ=100cm 
(c)f=2Hz 
(d)v=200cms 
(e)The dirrection of propagation of the wave is in the -ve direction of the x-axis 
(f)um=75.39cms 
(g)y=2cm

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