A transverse harmonic wave on a string is described by $y = 3 \sin \,(36t + 0.018x + \frac{\pi}{4})$ where $x$ and $y$ are in $cm$ and $t$ in $s$. The least distance between two sucessive crests in the wave is .... $m$
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${v_1}$ and ${v_2}$ are the velocities of sound at the same temperature in two monoatomic gases of densities ${\rho _1}$ and ${\rho _2}$ respectively. If $\frac{\rho _1}{\rho _2} = \frac{1}{4}$ then the ratio of velocities ${v_1}$ and ${v_2}$ will be
Two pulses travel in mutually opposite directions in a string with a speed of $2.5 cm/s$ as shown in the figure. Initially the pulses are $10cm$ apart. What will be the state of the string after two seconds
A string of length $0.4\, m$ and mass ${10^{ - 2}}\,kg$ is tightly clamped at its ends. The tension in the string is $1.6\, N.$ Identical wave pulses are produced at one end at equal intervals of time $\Delta t$. The minimum value of $\Delta t$ which allows constructive interference between successive pulses is .... $s$
$4.0 \,g$ of a gas occupies $22.4$ litres at $NTP.$ The specific heat capacity of the gas at constant volume is $5.0 \,\,J K^{-1} mol^{-1}$. If the speed of sound in this gas at $NTP$ is $952\, m s^{-1}$, then the heat capacity at constant pressure is .... $J K^{-1} mol^{-1}$ (Take gas constant $R = 8.3 \,\,J K^{-1} mol^{-1}$)
When two sound waves with a phase difference of $\pi /2$, and each having amplitude $A$ and frequency $\omega $, are superimposed on each other, then the maximum amplitude and frequency of resultant wave is
If two waves of same frequency and same amplitude respectively, on superimposition produced a resultant disturbance of the same amplitude, the waves differ in phase by
$Assertion :$ When a beetle moves along the sand within a few tens of centimeters of a sand scorpion, the scorpion immediately turns towards the beetle and dashes towards it
$Reason :$ When a beetle disturbs the sand, it sends pulses along the sand's surface. One set of pulses is longitudinal while the other set is transverse.