1) A fellow student of mathematical bent tells you that the wave function of a t
ID: 1507889 • Letter: 1
Question
1) A fellow student of mathematical bent tells you that the wave function of a traveling wave on a thin rope isy(x,t)= 2.10 mm cos[( 7.08 rad/m )x+( 750 rad/s )t].Being more practical-minded, you measure the rope to have a length of 1.30 m and a mass of 3.38 g .
a) Determine the tension in the rope.
b) Determine the average power transmitted by the wave.
2) Two small speakers A and B are driven in step at 740 Hz by the same audio oscillator. These speakers both start out 4.50 m from the listener, but speaker A is slowly moved away.
a) At what distance d will the sound from the speakers first produce destructive interference at the location of the listener?
b) If A keeps moving, at what distance d will the speakers next produce destructive interference at the listener?
c) After A starts moving away, at what distance will the speakers first produce constructive interference at the listener?
Explanation / Answer
1)
compare the given equation with
y(x,t) = A*cos(k*x + w*t)
k = 7.08 rad/m
w = 750 rad/s
we know, wave speed, v = w/k
= 750/7.08
= 105.9 m/s
linear mass density of string, mue = m/L = 3.38*10^-3/1.3
= 2.6*10^-3 kg/m
now Apply, v = sqrt(T/mue)
==> T = v^2*mue
= 105.9^2*2.6*10^-3
= 0.275 N <<<<<-----------Answer
b)
Avarge power transported = 0.5*mue*w^2*A^2*v
= 0.5*2.6*10^-3*750^2*(2.1*10^-3)^2*105.9
= 0.3415 Watts <<<<<-----------Answer
2)
a) for ditrcutive interefernce, d = lamda/2
= (v/f)/2
= (340/740)/2
= 0.23 m
b) when d = 3*(lamda/2)
= 3*(v/f)/2
= 3*(340/740)/2
= 3*0.23
= 0.69 m
c) d = lamda
= v/f
= 340/740
= 0.46 m
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