The equation of the progressive wave is `y = 3 sin[pi(t/3-x/5)+pi/4]` , where x and y are in metre and time in second. Which of the following is correct.

Options

A. Velocity v = 1.5 m/s
B. Amplitude A = 3 cm
C. Frequency F = 0.2 Hz
D. Wavelength `lamda = 10cm`

Answer

D

Explanation

`y = 3 sin [pi ((t)/(3) - (x)/(5)) + (pi)/(4)]`
This is written as
`y = 3 sin [2pi ((t)/(6) - (x)/(10)) + (pi)/(4)]`
Comparing this with the standard equation
`y = A sin [2pi ((t)/(T) - (x)/(lamda)) + (pi)/(4)]`, we get
(i) Amplitude = 3 m, 3 cm is wrong
(ii) Frequency `(n) = (1)/(T) = (1)/(3) = 0.33 Hz, 0.2 Hz` is wrong
(iii) Velocity `=n lamda = (1)/(3) xx 10 = (10)/(3) = 3.33 m//s`, hence v = 1.5 m/s is wrong
(iv) `lamda = 10 m, " thus " lamda = 10m` is the correct answer