A travelling wave moving from left to right has an amplitude of 0.15m, a frequency of 550Hz and a wavelength of 0.01m. The equation describing the wave is A. y = 0.15 sin 200π(x - 5.5t) B. y = 0.15 sin π(0.01x - 5.5t) C. y = 0.15 sin 5.5π(x - 200t) D. y = 0.15 sin π(550x - 0.01t)

Physics

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Answer

A

Step-by-step solution

4 steps

To find the equation describing the travelling wave, we use the general form for a wave moving from left to right:

y(x,t)=Asin⁡(kx−ωt)y(x, t) = A \sin(kx - \omega t)

where AA is the amplitude, kk is the wave number, and ω\omega is the angular frequency.

Given values:
Amplitude A=0.15 mA = 0.15 \, \text{m}
Frequency f=550 Hzf = 550 \, \text{Hz}
Wavelength λ=0.01 m\lambda = 0.01 \, \text{m}

  1. Calculate the wave number kk.

    The wave number kk is given by the formula k=2πλk = \frac{2\pi}{\lambda}.

    k=2π0.01 m=200π rad/mk = \frac{2\pi}{0.01 \, \text{m}} = 200\pi \, \text{rad/m}
  2. Calculate the angular frequency ω\omega.

    The angular frequency ω\omega is given by the formula ω=2πf\omega = 2\pi f.

    ω=2π(550 Hz)=1100π rad/s\omega = 2\pi (550 \, \text{Hz}) = 1100\pi \, \text{rad/s}
  3. Substitute the values of AA, kk, and ω\omega into the wave equation.

    y(x,t)=0.15sin⁡(200πx−1100πt)y(x, t) = 0.15 \sin(200\pi x - 1100\pi t)
  4. Compare this equation with the given options.

    Let's examine option A: y=0.15sin⁡200π(x−5.5t)y = 0.15 \sin 200\pi(x - 5.5t)
    Expand the term inside the sine function:

    200π(x−5.5t)=200πx−200π×5.5t200\pi(x - 5.5t) = 200\pi x - 200\pi \times 5.5t 200π×5.5=1100π200\pi \times 5.5 = 1100\pi

    So, option A becomes:

    y=0.15sin⁡(200πx−1100πt)y = 0.15 \sin(200\pi x - 1100\pi t)

    This matches the equation we derived.

    The final answer is A\boxed{\text{A}}.

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