Question

Which of the following is not true for this progressive wave $y=4\sin 2\pi (\frac{t}{0.02}-\frac{x}{100})$ where y and x are in cm & t in sec. [CMPT 2003]

• A. Its amplitude is 4 cm
• B. Its wavelength is 100 cm
• C. Its frequency is 50 cycles/sec
• D. Its propagation velocity is $50\times {10}^3$ cm/sec

Answer 1

The correct option is D Its propagation velocity is $50\times {10}^3$ cm/sec

The standard equation of a wave is given by,

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

Let's now convert the given equation into the standard wave equation.

$y=4sin2\pi (\frac{t}{0.02}-\frac{x}{100})$

or, $y=4sin(\frac{2\pi }{0.02}t-\frac{2\pi }{100}x)$

Comparing this with the standard equation we get,

$A=4,\omega =\frac{2\pi }{0.02},k=\frac{2\pi }{100}$

Amplitude is $4cm$ which is true, so option (A) is correct.

Wavelength, $\lambda =\frac{2\pi }{k}=\frac{2\pi }{\frac{2\pi }{100}}=100cm$. So, option (B) is also correct.

Frequency, $f=\frac{\omega }{2\pi }=\frac{\frac{2\pi }{0.02}}{2\pi }=50cycles/sec$. So, option (C) is also correct.

The propagation velocity, $v=\frac{\omega }{k}=\frac{\frac{2\pi }{0.02}}{\frac{2\pi }{100}}=5000cm/s=50\times {10}^{2}cm/s$. Hence option (D) is not true for this wave.

Hence Option is D