Question

A plane progressive wave cannot be represented by

• A. $y=a\,\sin(\omega t\pm\,kx)$
• B. $y=a\,\sin\,2\pi\left(\frac{l}{T}\mp\frac{x}{\lambda}\right)$
• C. $y=a\,\sin\frac{2\pi}{\lambda}(Vl\mp\,x)$
• D. y=A log x + Blog x

Answer 1

The Correct Option is D

A plane progressive wave is typically represented by equations involving sinusoidal functions of time and space.

A. \(y = a \sin(\omega t \pm kx)\):
This is a standard form representing a plane progressive wave, where \(\omega\) is the angular frequency, k is the wave number, t is time, and x is position.

B. \(y = a \sin \left( 2\pi \left( \frac{t}{T} \mp \frac{x}{\lambda} \right) \right)\):
This is also a valid representation of a plane progressive wave, where T is the period and \(\lambda\) is the wavelength.

C. \(y = a \sin \left( \frac{2\pi}{\lambda} (Vt \mp x) \right)\):
This is another valid form, where V represents the wave velocity, t is time, and x is position.

D. \(y = A \log x + B \log x\):
This equation is not a typical representation of a plane progressive wave. It involves logarithmic functions of x, which do not describe the oscillatory nature of a wave propagating through space and time.

So, the correct answer is (D): \(y = A \log x + B \log x\).