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

2023 · 1 Feb · Shift 1 · Q51
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. /2023 · 1 Feb · Shift 1 · Q51

Waves question

2023 · 1 Feb · Shift 1 · Q51

JEE MainPhysicsWavesMCQ+4 / −1
A steel wire with mass per unit length 7.0×10−3 kg m−17.0 \times 10^{-3} \mathrm{~kg} \mathrm{~m}^{-1}7.0×10−3 kg m−1 is under tension of 70 N70 \mathrm{~N}70 N. The speed of transverse waves in the wire will be:
  1. A
    10 m/s10 \mathrm{~m} / \mathrm{s}10 m/s
  2. B
    50 m/s50 \mathrm{~m} / \mathrm{s}50 m/s
  3. C
    100 m/s100 \mathrm{~m} / \mathrm{s}100 m/s
  4. D
    200π m/s200 \pi\mathrm{~m} / \mathrm{s}200π m/s
View written solutionFree

Correct answer: C

  1. For a stretched wire, the speed of transverse waves is

v=Tμv = \sqrt{\frac{T}{\mu}}v=μT​​

where:

  • T=70 NT = 70\,\text{N}T=70N is the tension,
  • μ=7.0×10−3 kg m−1\mu = 7.0 \times 10^{-3}\,\text{kg m}^{-1}μ=7.0×10−3kg m−1 is the mass per unit length.
  1. Substitute the given values:

v=707.0×10−3v = \sqrt{\frac{70}{7.0 \times 10^{-3}}}v=7.0×10−370​​

  1. Simplify inside the square root:

707.0×10−3=700.007=10000\frac{70}{7.0 \times 10^{-3}} = \frac{70}{0.007} = 100007.0×10−370​=0.00770​=10000

So,

v=10000=100 m/sv = \sqrt{10000} = 100\,\text{m/s}v=10000​=100m/s

  1. Compare with the options:
  • A: 10 m/s10\,\text{m/s}10m/s
  • B: 50 m/s50\,\text{m/s}50m/s
  • C: 100 m/s100\,\text{m/s}100m/s
  • D: 200π m/s200\pi\,\text{m/s}200πm/s

Hence, the correct option is:

C (100 m/s)\boxed{\text{C } (100\,\text{m/s})}C (100m/s)​

PreviousNext

More from Waves

  • An organ pipe 40 cm long is open at both ends. The speed of sound in air is 360 ms−1. The frequency of the second harmonic is ​Hz.2023 · Numerical
  • A guitar string of length 90 cm vibrates with a fundamental frequency of 120 Hz. The length of the string producing a fundamental frequency of 180 Hz will be ​ cm.2023 · Numerical
  • A transverse harmonic wave on a string is given by y(x,t)=5sin(6t+0.003x) where x and y are in cm and t in sec. The wave velocity is ​ ms −1.2023 · Numerical
  • For a periodic motion represented by the equation y=sinωt+cosωt the amplitude of the motion is2023 · MCQ
  • The equation of wave is given by Y=10−2sin2π(160t−0.5x+π/4) where x and Y are in m and t in s. The speed of the wave is ​km h−1.2023 · Numerical
  • For a certain organ pipe, the first three resonance frequencies are in the ratio of 1:3:5 respectively. If the frequency of fifth harmonic is 405 Hz and the speed of sound in air is 324 ms−1 the length of the…2023 · Numerical
  • In an experiment with sonometer when a mass of 180 g is attached to the string, it vibrates with fundamental frequency of 30 Hz. When a mass m is attached, the string vibrates with fundamental frequency…2023 · Numerical
  • The fundamental frequency of vibration of a string stretched between two rigid support is 50 Hz. The mass of the string is 18 g and its linear mass density is 20 g/m. The speed of the…2023 · Numerical