Question

A simple harmonic wave having an amplitude a and time period T is represented by the equation $y = 5\sin\pi(t + 4)m.$ Then the value of amplitude (1) in (m) and time period (T) in second are

• A. $a = 10,T = 2$
• B. $a = 5,T = 1$
• C. $a = 10,T = 1$
• D. $a = 5,T = 2$

Answer 1

Answer: (D)

$a = 5,T = 2$

Answer 2

$y = 5\sin(\pi t + 4\pi)$, comparing it with standard equation

$y = a\sin(\omega t + \varphi) = a\sin\left( \frac{2\pi t}{T} + \varphi \right)$

$a = 5m$ and $\frac{2\pi t}{T} = \pi t$ ⇒ T = 2 sec.