# 25 - Waves and Oscillations Questions Answers

A small ring is threaded on an inextensible frictionless cord of length 2l.  The ends of the cord are fixed to a horizontal ceiling.  In equilibrium, the ring is at a depth h below the ceiling.  Now the ring is pulled aside by a small distance in the vertical plane containing the cord and released.  If period of small oscillations of the ring is kπ, find k.  Given,

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Joshi sir comment
Joshi sir comment

small ring is threaded on an inextensible frictionless cord of length 2l.

The ends of the cord are fixed to a horizontal ceiling. In equilibrium, the

ring is at a depth h below the ceiling. Now the ring is pulled aside by a

small distance in the vertical plane containing the cord and released.

Find period of small oscillations of the ring. Acceleration of free fall is g.

Joshi sir comment

while measuring the speed of sound by performing a resonance column expt , a student gets d first resonance conditn at a column length of 18 cm during winter . Repeating d same expt during summer , she measure d column length to be x cm for the second resonance. THEN

1)18>X

2)X>54

3) 54>X>36

4) 36>X>18

ANS (2)

AIEEE 2008

Joshi sir comment

since l α λ α v/n          n is frequency

on increasing temperature, v increases so λ increases

for first resonance l = λ/4

and for third resonance L = 3λ'/4

and λ> λ so x will be more than 54

when a tuning fork vibrates with 1.0 m  or  1.05m long wire of a sonometer, 5 beats per second are produced in each case. what will be the frequency of the  tuning fork ??

Joshi sir comment

for sonometer wire

l = λ/2

or 2l = v/n                                    here n represents frequency

or n = v/2l

for first wire of 1 m length n= v/2

for second wire of 1.05 m length n=v/2.1

let frequency of tuning fork = n1

so according to the given condition v/2 = n1+ 5

and v/2.1 = n1 - 5

solve now

TWO PENDULUM HAVE TIME PERIODS T &5T/4. THEY STARTS SHM AT THE SAME TIME FROM THE MEAN POSITION . WHAT WILL BE THE PHASE DIFFERENCE B/W THEM AFTER D BIGGER PENDULUM COMPLETED ONE OSCILLATn ??

ans 900

Joshi sir comment

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

a cylinderical tube open at both ends has a fundamental frequency f in air the tube is dipped vertically in H2O so that half of it is in H2O the fundamental frequency of the air column is

1)f/2

2)3f/4

3)2f

4) f

aieee 2012

Joshi sir comment

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.

QUES  TWO IDENTICAL SOUNDS s1 &s2  reach at a point P in phase. resultant loudness at a point P is ndB higher than loudness of s1 the value of n =?

ANS) 6

Joshi sir comment

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/I= 10logI/I0+ 10log4

since 10log4 = 6 so increment = 6

## a uniformrope of lenth 10 m and mass 12 kg hangs verticaly from a rigid support .  a block of mass 4 kg is attached to the free end  of  the rope . atrans verse wave of wavelenth 00.03 m is prodused at the lower end .  wavelenth of pulse when it reaches upper end  will be?

Joshi sir comment

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.

2 comparable masses m1 and m2  r orbiting about their bodycenter o at distance r1 and r2 from  their  body center respectively  with a common period T. the squar of time period  ?

Joshi sir comment

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