Sign in
12thPass logo
New chatPYQ LibraryDoubtsRank report
Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →
Sign in

Waves question

2014 · Shift 0 · Q61
Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.
  1. PYQ Library
  2. /JEE Main
  3. /Physics
  4. /Waves
  5. /2014 · Shift 0 · Q61

Waves question

2014 · Shift 0 · Q61

JEE MainPhysicsWavesMCQ+4 / −1
A pipe of length 85cm85cm85cm is closed from one end. Find the number of possible natural oscillations of air column in the pipe whose frequencies lie below 1250Hz1250Hz1250Hz. The velocity of sound in air is 340m/s340m/s340m/s.
  1. A
    121212
  2. B
    888
  3. C
    666
  4. D
    444
View written solutionFree

Correct answer: C

  1. Natural frequencies of a closed pipe

For a pipe closed at one end, only odd harmonics are allowed.

The natural frequencies are:

fn=nv4L,n=1,3,5,7,…f_n = \frac{n v}{4L}, \quad n=1,3,5,7,\dotsfn​=4Lnv​,n=1,3,5,7,…

where:

  • v=340 m/sv = 340\,\text{m/s}v=340m/s
  • L=85 cm=0.85 mL = 85\,\text{cm} = 0.85\,\text{m}L=85cm=0.85m
  1. Find the fundamental frequency
f1=3404×0.85f_1 = \frac{340}{4 \times 0.85}f1​=4×0.85340​

Since

4×0.85=3.44 \times 0.85 = 3.44×0.85=3.4

so

f1=3403.4=100 Hzf_1 = \frac{340}{3.4} = 100\,\text{Hz}f1​=3.4340​=100Hz

Thus allowed frequencies are:

100,300,500,700,900,1100,1300,…100, 300, 500, 700, 900, 1100, 1300, \dots100,300,500,700,900,1100,1300,…
  1. Count frequencies below 1250 Hz1250\,\text{Hz}1250Hz

We need:

fn<1250f_n < 1250fn​<1250

Using

fn=100nf_n = 100nfn​=100n

with odd nnn,

100n<1250⇒n<12.5100n < 1250 \Rightarrow n < 12.5100n<1250⇒n<12.5

Odd integers less than 12.512.512.5 are:

1,3,5,7,9,111,3,5,7,9,111,3,5,7,9,11

Total number of possible natural oscillations:

666
  1. Check options
  • A: 121212 ❌
  • B: 888 ❌
  • C: 666 ✅
  • D: 444 ❌

Therefore, the correct answer is Option C.

PreviousNext

More from Waves

  • A sonometer wire of length 1.5m is made of steel. The tension in it produces an elastic strain of 1%. What is the fundamental frequency of steel if density and elasticity of steel are 7.7×103kg/m3 and 2.2×1011N/m2…2013 · MCQ
  • A cylindrical tube, open at both ends, has a fundamental frequency, f, in air. The tube is dipped vertically in water so that half of it is in water. The fundamental frequency of the air-column is now :2012 · MCQ
  • The transverse displacement y(x,t) of a wave on a string is given by y(x,t)=e−(ax2+bt2+2ab​xt). This represents a:2011 · MCQ
  • The equation of a wave on a string of linear mass density 0.04kgm−1 is given by y=0.02(m)sin[2π(0.04(s)t​−0.50(m)x​)]. The…2010 · MCQ
  • Three sound waves of equal amplitudes have frequencies (v−1),v,(v+1). They superpose to give beats. The number of beats produced per second will be :2009 · MCQ
  • A wave travelling along the x-axis is described by the equation y(x,t)=0.005 cos(αx−βt). If the wavelength and the time period of the wave are 0.08m and 2.0s, respectively, then α and β…2008 · MCQ
  • While measuring the speed of sound by performing a resonance column experiment, a student gets the first resonance condition at a column length of 18cm during winter. Repeating the same experiment during summer, she measures the column…2008 · MCQ
  • A sound absorber attenuates the sound level by 20dB. The intensity decreases by a factor of2007 · MCQ