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Concepts Of Physics MCQ Edition [Volume 1]
Exam
Concepts Of Physics MCQ Edition [Volume 1]
Subject
Physics
Chapter
Sound Waves

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Sound Waves

A travelling sound wave is described by the equation y = 6.0 (600 t...

A travelling sound wave is described by the equation y=6.0sin⁡(600t−1.8x)y = 6.0 \sin(600 t - 1.8 x), with yy measured in 10−5 m10^{-5} \text{ m}, tt in second, and xx in metre. Determine the ratio of the displacement amplitude of the particles to the wavelength of the wave.

Options

  1. A1.7×10−51.7 \times 10^{-5}
  2. B3.4×10−53.4 \times 10^{-5}
  3. C1.1×10−41.1 \times 10^{-4}
  4. D5.4×10−55.4 \times 10^{-5}

Correct answer

A. 1.7×10−51.7 \times 10^{-5}

Step-by-step solution

The given equation of the travelling sound wave is y=6.0sin⁡(600t−1.8x)y = 6.0 \sin(600 t - 1.8 x).

Comparing this with the standard wave equation y=Asin⁡(ωt−kx)y = A \sin(\omega t - k x), we get:
Displacement amplitude, A=6.0×10−5 mA = 6.0 \times 10^{-5} \text{ m}
Angular wave number, k=1.8 rad/mk = 1.8 \text{ rad/m}

The wavelength λ\lambda of the wave is given by:
λ=2πk=2π1.8=π0.9 m\lambda = \dfrac{2\pi}{k} = \dfrac{2\pi}{1.8} = \dfrac{\pi}{0.9} \text{ m}

The ratio of the displacement amplitude to the wavelength is:
Aλ=6.0×10−5π0.9=5.4×10−5π\dfrac{A}{\lambda} = \dfrac{6.0 \times 10^{-5}}{\dfrac{\pi}{0.9}} = \dfrac{5.4 \times 10^{-5}}{\pi}

Using π≈3.14\pi \approx 3.14, we get:
Aλ=5.4×10−53.14≈1.7×10−5\dfrac{A}{\lambda} = \dfrac{5.4 \times 10^{-5}}{3.14} \approx 1.7 \times 10^{-5}
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