$A$ sound source of frequency $170 \, Hz$ is placed near a wall. $A$ man walking from the source towards the wall finds that there is a periodic rise and fall of sound intensity. If the speed of sound in air is $340 \, m/s$,the distance (in metres) separating the two adjacent positions of minimum intensity is

$A$ string of length $1\,m$ and linear mass density $0.01\,kg/m$ is stretched to a tension of $100\,N$. When both ends of the string are fixed,the three lowest frequencies for standing waves are $f_1, f_2$,and $f_3$. When only one end of the string is fixed,the three lowest frequencies for standing waves are $n_1, n_2$,and $n_3$. Then:

The equation of a stationary wave on a string clamped at both ends and vibrating in the third harmonic is $Y = 0.5 \sin(0.314 x) \cos(600 \pi t)$,where $x$ and $y$ are in $cm$ and $t$ is in seconds. The length of the vibrating string is: (in $cm$)

The equation $y = 0.15 \sin(5x) \cos(300t)$ describes a stationary wave. The wavelength of the stationary wave is .... $m$.

At a certain instant,a stationary transverse wave is found to have maximum kinetic energy. The appearance of the string at that instant is:

$A$ wave disturbance in a medium is described by $y(x, t) = 0.02 \cos(50 \pi t + \frac{\pi}{2}) \cos(10 \pi x)$,where $x$ and $y$ are in metres and $t$ is in seconds.