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 amplit

Question

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. What are the:

a. Speed
b. Wavelength of the wave?
c. Write down a mathematical expression for the wave, substituting numbers for the variables

in progress 0
Diễm Thu 4 years 2021-08-21T16:35:45+00:00 1 Answers 70 views 0

Answers ( )

  1. danthu
    0
    2021-08-21T16:37:39+00:00
    Reply

    Answer:

    (a) The speed of the wave, v is 4.2 m/s

    (b) Wavelength of the wave, λ is 0.35 m

    (c) mathematical expression of the wave, Y = 0.036sin(5.71πx – 24πt)

    Explanation:

    Given;

    tension on the string, T = 15 N

    Linear density, μ = 0.85 kg/m

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

    frequency of the wave, f = 12 Hz

    (a) The speed of the wave, v is calculated as;

    v = \sqrt{\frac{T}{\mu} } \\\\v = \sqrt{\frac{15}{0.85} }\\\\v = 4.2 \ m/s

    (b) Wavelength of the wave, λ

    v = fλ

    λ = v / f

    λ = 4.2 / 12

    λ = 0.35 m

    (c) mathematical expression of the wave;

    Y = Asin(\frac{2\pi x}{\lambda} -\omega t)\\\\Y = Asin(\frac{2\pi x}{\lambda} -2\pi f t)\\\\Y = 0.036sin (\frac{2\pi }{0.35}x -2\pi *12 t)\\\\Y = 0.036sin (5.71 \pi x - 24 \pi t)

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )