Question

Standing wave is formed by the superposition of two waves travelling in opposite directions. The transverse displacement is given by

y(x,t)=0.5sin(5π4x)cos(200πt)
What is the speed of the travelling wave moving in the positive x direction?
(x and t are in meter and second, respectively)
(A) 120m/s
(B) 180m/s
(C) 90m/s
(D) 160m/s

Answer 1

The speed of the traveling wave in the positive x direction is 160 m/s.(option D)

Step-by-step explanation:

The transverse displacement of a standing wave is given by the equation y(x,t) = 0.5sin(5π/4x)cos(200πt). To determine the speed of the traveling wave in the positive x direction, we need to find the frequency and wavelength of the wave. The frequency is given by the coefficient of 't' in the equation, which is 200π. Using the equation v = fλ, where 'v' is the speed of the wave, 'f' is the frequency, and 'λ' is the wavelength, we can calculate the speed.

Since the frequency is 200π, and the wavelength can be calculated as λ = 2π/k, where 'k' is the coefficient of 'x' in the equation, which is 5π/4, we can substitute the values into the equation v = fλ.

Thus, v = (200π)(2π / (5π/4)) = 160 m/s. Therefore, the speed of the traveling wave in the positive x direction is 160 m/s (option D).