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The equation of a travelling sound wave is y = 6.0 sin (600 t – 1.8 x) where y is measured in 10–5 m, t in second and x in metre. (a) Find the ratio of the displacement amplitude of the particles to the wavelength of the wave. (b) Find the ratio of the velocity amplitude of the particles to the wave speed.
Here given r base y = 6.0 * 10^-5 m a) Given 2π/λ = 1.8 ⇒ λ = (2π/1.8) So, r base y/ π = 6.0 * (1.8) * 10^-5 m/s /2π = 1.7 * 10^-5 m b) Let, velocity amplitude = V base y V = dy/dt = 3600 cos (600 t – 1.8) × 10^–5 m/s Here V base y = 3600 × 10^–5 m/s Again, λ = 2π/1.8 and T = 2π/600 ⇒ wave speed = v = λ/T = 600/1.8 = 1000 / 3 m/s. So the ratio of (V base y/v) = 3600 * 3 *10^-5/1000
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