Waves and its Characteristics: Practice Problem & Solution
Two waves represented by the following equations are travelling in the same medium: \(y_1 = 5 \sin 2\pi(75t - 0.25x)\) and \(y_2 = 10 \sin 2\pi(150t - 0.50x)\). The intensity ratio \(I_1/I_2\) of the two waves is:
Solution Explained:
To solve this problem, we apply the core principles of Waves and its Characteristics. Understanding the underlying formula is key to arriving at the correct answer below:
The intensity of a wave is proportional to the square of its amplitude and frequency, \(I \propto A^2 f^2\). Substituting \(A_1=5, f_1=75\) and \(A_2=10, f_2=150\) gives \(\frac{I_1}{I_2} = \left(\frac{5}{10}\right)^2 \left(\frac{75}{150}\right)^2 = \frac{1}{16}\).
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