Question

A wave is represented by the equation
y=(0·001 mm) sin[(50 s-1)t+(2·0 m-1)x].
(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

The Amplitude is 0.001 mm

Explanation:

(c) The frequency = 25/π Hz.

(d) The amplitude = 0⋅001 mm.

$y = (0.001 mm) sin[(50 s^-^1)t + (2.0 m^-^1)x]$

Equating the above equation with general equation, we get:

$y = Asin (\omega t - kx)$

$\omega = \frac {2\pi}{T} = 2\pi v$

$k = \frac {2\pi}{\lambda}$

• Here, A is the amplitude,
• $\omega$ is the angular frequency,
• k is the wave number and
• $\lambda$ is the wavelength.

A = 0.001 mm

Now, $50 = 2\pi v$

Hence, $v = \frac {25}{\pi} Hz$