A wave travelling along the $x- $ axis is described by the equation $y(x, t) = 0.005\,\,cos(\alpha x\,-\,\beta t).$ If the wavelength and the time period of the wave are $0.08 \,\,m$ and $2.0\,\,s,$ respectively, then $\alpha $ and $\beta $ in appropriate units are
$\alpha \,\, = \,25.00\,\pi \,\, ;\,\,\beta \, = \,\pi $
$\alpha \,\, = \frac{{0.08}}{\pi }\,\, ;\,\,\beta \, = \,\frac{{2.0}}{\pi }$
$\alpha \,\, = \frac{{0.04}}{\pi }\,\, ;\,\,\beta \, = \,\frac{{1.0}}{\pi }$
$\alpha \,\, = 12.50\pi \,\, ;\,\,\beta \, = \,\frac{\pi }{{2.0}}$
Two tuning forks $A$ and $B$ produce $8\, beats/s$ when sounded together. $A$ gas column $37.5\, cm$ long in a pipe closed at one end resonate to its fundamental mode with fork $A$ whereas a column of length $38.5 \, cm$ of the same gas in a similar pipe is required for resonance with fork $B$. The frequencies of these two tuning forks, are
If $L_1$ and $L_2$ are the lengths of the first and second resonating air columns in a resonance tube, then the wavelength of the note produced is
Two tuning forks having frequency $256\, Hz \,(A)$ and $262\, Hz \,(B)$ tuning fork. $A$ produces some beats per second with unknown tuning fork, same unknown tuning fork produce double beats per second from $B$ tuning fork then the frequency of unknown tuning fork is :- ............ $\mathrm{Hz}$
A train whistling at constant frequency is moving towards a station at a constant speed $V$. The train goes past a stationary observer on the station. The frequency $n'$ of the sound as heard by the observer is plotted as a function of time $t (Fig.)$ . Identify the expected curve
Fundamental frequency of sonometer wire is $n$. If the length, tension and diameter of wire are tripled, the new fundamental frequency is