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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.

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.

Grade:10

1 Answers

Kevin Nash
askIITians Faculty 332 Points
8 years ago
Sol. 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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