A 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 positions of the peak of the pulse at t = 0 , 1 s , and 2 s r

Question

A 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 positions of the peak of the pulse at t = 0 , 1 s , and 2 s respectively.

Quantrex Academy · Accepted Answer

Correct answer: B. x = 0 , x = 20 cm , and x = 40 cm

The equation of the pulse is y = a^3 (x - vt)^2 + a^2 . The peak of the pulse occurs where the displacement y is maximum. This happens when the denominator is minimum, which corresponds to (x - vt)^2 = 0 . Thus, the position of the peak at any time t is given by x = vt . Given the velocity of the pulse v = 20 cm s ⁻¹ . At t = 0 , the position of the peak is x = 20 0 = 0 . At t = 1 s , the position of the peak is x = 20 1 = 20 cm . At t = 2 s , the position of the peak is x = 20 2 = 40 cm .

A 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 positions of the peak of the pulse at t = 0 , 1 s , and 2 s respectively.

Options

Correct answer

Step-by-step solution

More from Wave Motion and Waves on a String