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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 velocity amplitude of the particles to the wave speed.

Options

  1. A2.2×10−42.2 \times 10^{-4}
  2. B1.7×10−51.7 \times 10^{-5}
  3. C3.6×10−23.6 \times 10^{-2}
  4. D1.1×10−41.1 \times 10^{-4}

Correct answer

D. 1.1×10−41.1 \times 10^{-4}

Step-by-step solution

The given equation of the wave is y=6.0×10−5sin⁡(600t−1.8x)y = 6.0 \times 10^{-5} \sin(600 t - 1.8 x).

Comparing with the standard wave equation y=Asin⁡(ωt−kx)y = A \sin(\omega t - k x), we get:
A=6.0×10−5 mA = 6.0 \times 10^{-5} \text{ m}
ω=600 rad/s\omega = 600 \text{ rad/s}
k=1.8 m−1k = 1.8 \text{ m}^{-1}

The velocity amplitude of the particles is given by vm=Aωv_m = A \omega.

The wave speed is given by v=ωkv = \dfrac{\omega}{k}.

The ratio of the velocity amplitude of the particles to the wave speed is:
Ratio=vmv=Aωω/k=Ak\text{Ratio} = \dfrac{v_m}{v} = \dfrac{A \omega}{\omega / k} = A k

Substituting the values:
Ratio=(6.0×10−5)×1.8=10.8×10−5=1.08×10−4≈1.1×10−4\text{Ratio} = (6.0 \times 10^{-5}) \times 1.8 = 10.8 \times 10^{-5} = 1.08 \times 10^{-4} \approx 1.1 \times 10^{-4}
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