Question

Equation of progressive wave is given by $y=a\sin \pi (\frac{t}{2}-\frac{x}{4})$,where t is in seconds and x is in meter. Then the distance through which the wave moves in 4 seconds is (in meter)-

• A. $4m$
• B. $2m$
• C. $16m$
• D. $8m$

Answer 1

The correct option is B $2m$

y=a sin$\pi (\frac{t}{2}-\frac{x}{4})$

Compare this with standard equation, y=A sin 2$\pi (\frac{t}{T}-\frac{x}{\lambda })$

where, A= amplitude

$\lambda$= wavelength = 4

T= time period = 2

$\frac{1}{T}=\frac{1}{2}=0.5$

f= frequency

$f=\frac{1}{T}=0.5$

f= 0.5 Hz

Wave velocity, $v=f\times \lambda$

$v=0.5\times 4=2cm/s$