Progressive Wave in a String: Practice Problem & Solution
A transverse wave is represented by $y = A\sin(\omega t - kx)$. For what value of the wavelength is the wave velocity equal to the maximum particle velocity? (2010 Pre)
Solution Explained:
To solve this problem, we apply the core principles of Progressive Wave in a String. Understanding the underlying formula is key to arriving at the correct answer below:
The maximum particle velocity is $v_{max} = A\omega$. The wave velocity is $v = \omega/k$. Equating the two gives $\omega/k = A\omega$, so $1/k = A$. Since $k = 2\pi/\lambda$, we get $\lambda/(2\pi) = A$, which yields $\lambda = 2\pi A$.
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