Question

A wave is represented by the equation
\[y = \left( 0 \text{ cdot 001 mm }\right) \sin\left[ \left( 50 s^{- 1} \right)t + \left( 2 \cdot 0 m^{- 1} \right)x \right]\]
(a) The wave velocity = 100 m s⁻¹.
(b) The wavelength = 2⋅0 m.
(c) The frequency = 25/π Hz.
(d) The amplitude = 0⋅001 mm.

Answer 1

(c) Frequency = 25/π Hz
(d) Amplitude = 0⋅001 mm
\[y = \left( 0 \cdot 001 mm \right) \sin\left[ \left( 50 s^{- 1} \right)t + \left( 2 \cdot 0 m^{- 1} \right)x \right]\]
Equating the above equation with the general equation, we get:
\[y = A\sin\left( \omega t - kx \right)\]
\[\omega = \frac{2\pi}{T} = 2\pi v\]
\[k = \frac{2\pi}{\lambda}\]
Here, A is the amplitude, ω is the angular frequency, k is the wave number and λ is the wavelength.

\[A = 0 . 001  mm\] 

\[Now, \] 

\[50 = 2\pi\nu\] 

\[ \Rightarrow \nu = \frac{25}{\pi}  Hz\]