1. a nearly frictionless mass-spring oscillator with a period of 4sec is set int

Question

1. a nearly frictionless mass-spring oscillator with a period of 4sec is set into motion at t=0 with an initial maximum amplitude of 40cm. After t=100 sec , the maximu amplitude has decreased to 20cm. At what time will the amplitude have decreased to 5cm?

answer: t=300 sec

2. when an auditorium has a solid wall, sound waves will tend to perfectly reflect off the walll (with a 180 degree phase change). If listening to music, as from an orchestra, the incoming and reflected waves will interfere with each other. for a listener sitting 0.5m from the wall what is the lowest frequency wich gets suppressed by this interference?

answer: 165 Hz

3. A microwave oven works by producing standing wavesof leectromagnetic radiation inside a closed housing. Consider a microwave oven which is 30cm wide and which has five standing wave nodes-one at each end of the microwave plus three insdie the oven itself. what does the frequency of the radiation need to be to produce this pattern?

answer: 2.0*10^9 Hz

can you explain this???

Explanation / Answer

1) A = A0 e^(-kt)

so 40 = 20 *e^(-k*100)

k=-0.00693

5 = 40 e^(-0.00693*t)

t=300 s

2) to intefere PLD = lambda/2

PLD = 2*0.5 = lambda /2

lambda = 2

lambda f = v

f = 330/2 = 165 Hz

3) with 5 nodes

L = 2lambda

lambda = 15 cm = .15 m

lambda f = v

f = 3E8/.15 = 2.0E9 Hz

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