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Question

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Q3:: A string with a length of 2.50 m has two adjacent resonances at frequencies 112 Hz and 140 Hz. Determine the wavelength of the 112 Hz resonance. (Ans: 1.25 m)

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Q5:: A stone is dropped into a lake; and it produces circular surface waves with a frequency of 0.25 Hz. When should a second stone be dropped, after the first, at the same place to produce destructive interference? Ignore the time it takes the stone to reach water. (Ans: 2.0 s)

Please I have the basic steps to solve these but I want it in much deails AS POSSIBLE .

Explanation / Answer

1)Frequency=speed/wavelength= 2*f0

Power becomes 4 times due to doubling frequency and twice due to doubling speed.

P=(2)^2*2*50W=400W

2)Harmonic number=2L/lamda=2/0.4=5 (0.4 because 1/2.5=0.4)

3)L=n*lamda1/2

L=(n+1)*lamda2/2

v=lamda/f

f1=v/lamda1

lamda1=f1/v

lamda2=f2/v

2.5=n*140/2v(inverse relationship)

2.5=(n+1)*112/2v

v=112m/s,n=4

lamda1=2L/n=5/4=1.25m

4)2pi/lamda=15.7

lamda=0.40m

phase difference=60 degrees

path difference=Lamda/6=0.067m

5)Path difference for destructive interference=lamda/2

the cycle for the first wave has a minimum at T/2=2/f=2s. This is when the second stone should be dropped.

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