A wave propagates on a string in the positive x-direction at a velocity υ. The shape of the string at t = t₀ is given by g(x, t₀) = A sin(x/a). Write the wave equation for a general time t.

The displacement of the particle at x = 0 of a stretched string carrying a wave in the positive x-direction is given by f(t) = A sin(t/T). The wave speed is υ. Write the wave equation.

A wave pulse is travelling on a string with a speed υ toward the position X-axis. The shape of the string at t = 0 is given by g(x) = A sin (x/a), where A and a are constants.

(A) What are the dimensions of A and a? (B) Write the equation of the wave for a general time t, if the wave speed is υ.

The equation of a wave travelling on a string is

y = (010 mm) sin[(314 m⁻¹) x+ (314 s⁻¹) t].

(A) In which direction does the wave travel? (B) Find the wave speed, the wavelength and the frequency of the wave. (C) What is the maximum displacement and the maximum speed of a portion of the string?

A wave travels along the position x-direction with a speed of 20 m s⁻¹. The amplitude of the wave is 020 cm and the wavelength 20 cm. (A) Write a suitable wave equation which describes this wave. (B) What is the displacement and velocity of the particle at x = 20 cm at time t = 0 according to the wave equation written? Can you get different values of this quantity if the wave equation is written in a different fashion?