Question

Two second wave travel out from a common point have frequencies 30 Hz and 40 Hz respectively where phase difference between the after 0.8 second. ?

• A. zero
• B. $\frac{\pi }{4}$
• C. $\frac{5\pi }{2}$
• D. $5\pi$

Answer 1

The correct option is A zero

The phase of a travelling wave is given by $\varphi =Wt$, where $w=2\pi v$

so for the two waves.

$\varphi =2\pi v_{1}t$

$\varphi =2\pi v_{2}t$

given $v_1=30Hz$ and $v_2=40Hz$, at $t=0.8s$

${\varphi }_1=2\pi \left(30\right)\times 0.8$ ${\varphi }_2=2\pi \left(40\right)\times 0.8$

$=48\pi$ $=64\pi$

Thus phase difference

$\Delta \varphi ={\varphi }_2-{\varphi }_1=64\pi -48\pi =\perp \pi$, which is identically zero.

[$\varphi =m\pi ,m\in z$ are all equivalent angles]