A wave is represented by the equation y = 0.5 sin 0.4\pi(X - 60t), where the distance (X) is measured in centimetres and time (t) in seconds. What is the wavelength of the wave?
A
0.2cm
B
0.4cm
C
0.8cm
D
5.0cm
E
10.0cm
Verified Correct Answer: D.
Physical Principles & Numerical Solution
The general equation for a wave is given by y = Asin(k(x−vt)), where A is the amplitude, k is the wave number, v is the wave speed, and x and t are the position and time, respectively.
The wave number k is related to the wavelength \lambda by the equation k = \(\frac{2\pi}{\lambda}\)
In the given wave equation, y=0.5sin(0.4\pi(x−60t)), the wave number k is 0.4\pi.
Setting k = \(\frac{2\pi}{\lambda}\) equal to 0.4\pi and solving for \lambda gives:
\lambda = \(\frac{2\pi}{0.4\pi}\) = 5cm
So, the wavelength of the wave is 5 cm.
Source: Myschool Past Questions Archive (Record #42854)