30 - Waves and Oscillations Questions Answers

When bigger pendulum will complete its one oscillation, the smaller one will complete [1+(1/4)] oscillation. so phase difference = 2π*(T/4)/T = π/2

for first case       l = λ/2      so l = v/2f                

for second case l/2 = λ/4  so  l/2 = v/4f   

so f in both case are same.

Let intensity of one source = I

then intensity at a point where two waves meet in phase = I+I+2√I√Icos0 = 4I

now loudness = 10logI/I₀ due to a single source

and loudness at the point where 2 waves meet in phase = 10log4I/I₀ = 10logI/I₀+ 10log4

since 10log4 = 6 so increment = 6 

at top point tension in the string = 16g

and at bottom point T = 4g

and v = √(T/m)   here m is mass per unit length which is same throughout the rope.

first calculate v at both the points

frequency will be same throughout 

so use the formula v = nλ twice 

once at bottom and once at top point

then by diving these 2 formulae we will get the result

try it.

According to the diagram 

Gm₁m₂/(r₁+r₂)² = m₁r₁ω² = m₂r₂ω²

compare first part with either second or third part of the given equation for getting ω² then find T²

Intensity of a wave depends on two power of amplitude and two power of frequency. Check the graph carefully for getting idea about frequency and details of amplitude are given in the question.

I₁/I₂ = 4/1 so a₁/a₂ = 2/1 so a_max/ a_min = 2+1/2-1 = 3/1 so I_max/ I_min= 9/1

now loudness L = 10 log(I/I₀)

so difference of loudness = L₁-L₂ = 10 log (9I/I) = 10 log9 = 20 log3 

for maxima path diffrence should be integral multiple of λ.

It is given that two coherent light sources A and B with seperation 2λ are placed on the x-axis symmetrically about the origin, and we have to get the points of maxima in the circle so at the point where circle cuts the X axis (path diffrence = 2λ) and where circle cuts the Y axis (path difference = 0) will be the point of maxima. Besides it one point will also be present in the circle in first quadrant where path difference will be λ so it will be a maxima also. it means total 8 points are there

Use the formule I = I₁ + I₂ + 2 √I₁ √I₂ cosθ

here θ = 0

Use the formule I = I₁ + I₂ + 2 √I₁ √I₂ cosθ

here θ = 0