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30 July, 14:32

The tension in a string is 15 N, and its linear density is 0.85 kg/m. A wave on the string travels toward the - x direction; it has an amplitude of 3.6 cm and a frequency of 12 Hz.

(a) What are speed and wavelength of the wave?

(a) Write down the mathematical expression for the wave.

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  1. 30 July, 15:00
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    a) v = 4.20 m/s, 0.35 m

    b) y = 0.036sin (24πt + 17.94x)

    Explanation:

    Given:

    Tension in the string, T = 15 N

    Linear density of the string, M = 0.85 kg/m

    Amplitude of the wave, A = 3.6 cm = 0.036 m

    Frequency of the wave, f = 12 Hz

    a) now,

    the speed (v) of the wave is given as:

    v = √ (T/M)

    on substituting the values, we get

    v = √ (15/0.85)

    or

    v = 4.20 m/s

    also, wavelength (λ) is given as:

    λ = v/f

    on substituting the values, we get

    λ = 4.20/12

    or

    λ = 0.35 m

    b) The mathematical expression for the wave is given as:

    y = Asin (2πft + (2π/λ) x)

    thus,

    on substituting the values, we get

    y = 0.036sin (2π*12*t + (2π/0.35) x)

    or

    y = 0.036sin (24πt + 17.94x)
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