1) A fellow student of mathematical bent tells you that the wave function of a t

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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