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

A wave travelling on a string has the equation y = (0.10 mm ) [(31.4 m ⁻¹)x + (314 s ⁻¹)t] . Determine the wave speed, the wavelength and the frequency of the wave.

Options

  1. A10 m s ⁻¹ , 10 cm , 100 Hz
  2. B5 m s ⁻¹ , 40 cm , 25 Hz
  3. C20 m s ⁻¹ , 20 cm , 50 Hz
  4. D10 m s ⁻¹ , 20 cm , 50 Hz

Correct answer

D. 10 m s ⁻¹ , 20 cm , 50 Hz

Step-by-step solution

Comparing the given wave equation y = (0.10 mm ) [(31.4 m ⁻¹)x + (314 s ⁻¹)t] with the standard wave equation y = A (kx + t) , we get: k = 31.4 m ⁻¹ and = 314 s ⁻¹ The wave speed is given by v = k v = 314 31.4 = 10 m s ⁻¹ The wavelength is given by = 2 k = 2 3.14 31.4 = 0.2 m = 20 cm The frequency is given by f = 2 f = 314 2 3.14 = 50 Hz Thus, the wave speed is 10 m s ⁻¹ , wavelength is 20 cm and frequency is 50 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 -direction has its maximum located at x = 0 when t = 0 . Where will this maximum be found at t = 5 s A wave travelling on a string stretched along the X -axis has an equation given by y = A , e^ - ( x a + t T )^2 . Identify the direction in which the wave is travelling.A wave travelling on a string stretched along the X -axis has an equation given by y = A , e^ - ( x a + t T )^2 . Locate the maximum of the pulse at t = T and at t = 2T respectivelA wave travelling on a string stretched along the X -axis has an equation given by y = A , e^ - ( x a + t T )^2 . Determine the dimensions of A , a , and T .A wave travelling on a string stretched along the X -axis has an equation given by y = A , e^ - ( x a + t T )^2 . Compute the wave speed.A stretched string carries a wave in the positive x -direction with a wave speed of v . The displacement of the particle at x = 0 is described by f(t) = A (t/T) . Determine the wavA pulse travelling on a string is described by the function y = a^3 (x - vt)^2 + a^2 , where a = 5 mm and v = 20 cm s ⁻¹ . Taking x = 0 at the middle of the string, determine the pThe figure displays a wave pulse at t = 0 . The pulse travels to the right with a speed of 10 cm s ⁻¹ . Determine the respective rightward shifts of the shape of the string at t = Full Wave Motion and Waves on a String list All Concepts Of Physics MCQ Edition [Volume 1] PYQs