Question

A wave on a string passes the point x = 0 with amplitude A₀, angular frequency ω₀ and average rate of energy transfer P₀. As the wave travels down the string it gradually loses energy and at the point x = l the average rate of energy transfer becomes $\frac{P_{0}}{2}$. At the point x = £angular frequency and amplitude are respectively:

• A. ω₀ and A₀/√2
• B. ω ₀/√2 and A₀
• C. Less than ω₀ and A₀
• D. ω ₀/√2and A₀/√2

Answer 1

Answer: (A)

ω₀ and A₀/√2

Answer 2

P = $\frac{1}{2}\mu\omega$²A²v

speed $\left( \sqrt{\frac{T}{\mu}} \right)$will not change as both T and µ are constant, ω will also not change as it is property of the source that is causing the wave motion. Hence to make power half, amplitude becomes A₀/√2.