Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Concepts Of Physics MCQ Edition [Volume 1]
Exam
Concepts Of Physics MCQ Edition [Volume 1]
Subject
Physics
Chapter
Wave Motion and Waves on a String

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Wave Motion and Waves on a String

A string fixed at both ends is vibrating in its third harmonic. The...

A string fixed at both ends is vibrating in its third harmonic. The equation for its vibration is given by y=(0.4 cm)sin⁡[(0.314 cm−1)x]cos⁡[(600π s−1)t]y = (0.4 \text{ cm}) \sin[(0.314 \text{ cm}^{-1}) x] \cos[(600\pi \text{ s}^{-1})t]. Determine the frequency of vibration.

Options

  1. A150 Hz150 \text{ Hz}
  2. B300 Hz300 \text{ Hz}
  3. C1200 Hz1200 \text{ Hz}
  4. D600 Hz600 \text{ Hz}

Correct answer

B. 300 Hz300 \text{ Hz}

Step-by-step solution

The standard equation of a standing wave is given by y=Asin⁡(kx)cos⁡(ωt)y = A \sin(kx) \cos(\omega t).

Comparing the given equation y=(0.4 cm)sin⁡[(0.314 cm−1)x]cos⁡[(600π s−1)t]y = (0.4 \text{ cm}) \sin[(0.314 \text{ cm}^{-1}) x] \cos[(600\pi \text{ s}^{-1})t] with the standard equation, we get the angular frequency ω=600π rad/s\omega = 600\pi \text{ rad/s}.

The frequency of vibration is given by f=ω2πf = \dfrac{\omega}{2\pi}.

Substituting the value of ω\omega, we get f=600π2π=300 Hzf = \dfrac{600\pi}{2\pi} = 300 \text{ Hz}.
Practice Wave Motion and Waves on a String on Quantrex Academy →

More from Wave Motion and Waves on a String

A wave pulse travelling on a string at a speed of 40 cm s^ -1 in the negative x… Concepts Of Physics MCQ Edition [Volume 1]A wave travelling on a string stretched along the X -axis has an equation given by y =… Concepts Of Physics MCQ Edition [Volume 1]A wave travelling on a string stretched along the X -axis has an equation given by y =… Concepts Of Physics MCQ Edition [Volume 1]A wave travelling on a string stretched along the X -axis has an equation given by y =… Concepts Of Physics MCQ Edition [Volume 1]A wave travelling on a string stretched along the X -axis has an equation given by y =… Concepts Of Physics MCQ Edition [Volume 1]A stretched string carries a wave in the positive x -direction with a wave speed of v .… Concepts Of Physics MCQ Edition [Volume 1]A pulse travelling on a string is described by the function y = (a^3)/((x - vt)^2 + a^2)… Concepts Of Physics MCQ Edition [Volume 1]The figure displays a wave pulse at t = 0 . The pulse travels to the right with a speed… Concepts Of Physics MCQ Edition [Volume 1] Full Wave Motion and Waves on a String list All Concepts Of Physics MCQ Edition [Volume 1] PYQs