Question

The equation of progressive wave in a wire is given by $y=0.15sin\left[2\pi (15t-\frac{x}{10})\right]$
Where the distance is in meters and time in seconds.
Determine i) amplitude, ii) frequency, iii) wavelength and iv) velocity of the wave

• A. $A=0.15m,f=150Hz,v=150m/s,\lambda =1m$
• B. $A=0.1m,f=15Hz,v=15m/s,\lambda =1m$
• C. $A=0.15m,f=15Hz,v=150m/s,\lambda =10m$
• D. $A=0.15m,f=30Hz,v=15m/s,\lambda =10m$

Answer 1

The correct option is C $A=0.15m,f=15Hz,v=150m/s,\lambda =10m$

$y=0.15sin\left[2\pi (15t-\frac{x}{10})\right]=0.15sin\left[30\pi (t-\frac{x}{150})\right]$
Comparing with standard wave equation $y=Asin\left[\omega (t-\frac{x}{v})\right]$, we get
$A=0.15m,f=\frac{\omega }{2\pi }=\frac{30\pi }{2\pi }=15Hz,v=150m/s,\lambda =\frac{v}{f}=10m$