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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Asked By: ANOUSHKA
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Asked By: TUSHAR GUPTA
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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.

Asked By: ABHISHEK KHANDELWAL
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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

Asked By: SARIKA SHARMA
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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 ??

Asked By: SARIKA SHARMA
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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

Asked By: SARIKA SHARMA
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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

Asked By: SARIKA SHARMA
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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

Asked By: SARIKA
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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?

 

 

Asked By: SHUBHAM VED
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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  ?

Asked By: SHUBHAM VED
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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

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