Question

When a stationary wave is formed, then its frequency is

• A. Same as that of the individual waves
• B. Twice that of the individual waves
• C. Half that of the individual waves
• D. That of the individual waves

Answer 1

The correct option is A Same as that of the individual waves

Let us consider a progressive wave of amplitude $a$ , wavelength $\lambda$ and frequency $f=\frac{1}{T}$ travelling in the direction of $X$- axis whose equation is given by-

$y_1=a\sin \left(2\pi \right[\frac{t}{T}-\frac{x}{\lambda }])$

This wave is reflected from a free end and it travels in the negative direction of $X$- axis with frequency $f=\frac{1}{T}$

$y_1=a\sin \left(2\pi \right[\frac{t}{T}+\frac{x}{\lambda }])$

According to principle of superposition

$\Rightarrow y_1+y_2=a\sin \left(2\pi \right[\frac{t}{T}-\frac{x}{\lambda }])+a\sin \left(2\pi \right[\frac{t}{T}+\frac{x}{\lambda }])$

$\Rightarrow y_1+y_2=a\sin \left(\frac{2\pi t}{T}\right)\cos \left(\frac{2\pi x}{\lambda }\right)$

Here we can see the frequency of resultant wave is also $f=\frac{1}{T}$.