Two transverse waves of equal has a amplitude, frequency and wavelenght, travlin
ID: 1953644 • Letter: T
Question
Two transverse waves of equal has a amplitude, frequency and wavelenght, travling in opposite directions on a string generate a standing wave. The string lenght is 10m. Both ends of the string are tightly attached to a wall. There are 4 antinodes in the generated standing wave. The oscillatory (temporal) term of the standing wave has a frequency of 15Hz.A). What is the wavelenght of the standing wave?
B). If the maxium amplitude of the standing wave is 7cm, write the complete expressions, including values for k and w, for the "parent" waves (that generated the standing wave) travling to the right and travling to the left. The right direction is assumed as the + x direction?
C). Write the expression for the standing wave?
Explanation / Answer
a)as 4 antinodes formed and distance between consecutive antinodes=/2
as the waves will be within the string itself,
4*/2=L [L=length of string]
=L/2
=10/2
=5m
wave length=5m
b)f=15Hz,Amax=7cm
w=2*pi*f
=2*3.14*15
=94.2s^-1
k=2*pi/
=2*3.14/5
=1.256m^-1
speed of standing wake,V=w/k
=94.2/1.256
=75m/s
let y1=Asin(kx-wt) [wave travelling right]
=3.5sin(1.256x-94.2t)
y2=Asin(kx+wt) [wave travelling left]
=3.5sin(1.256x+94.2t)
y=y1+y2
=2Asin(kx)cos(wt)
2A=7
A=3.5cm
the equation of standing wave,y=7sin(1.256x)cos(94.2t) in cm
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