The equation of a progressive wave is $y = 8\sin \left[ {\pi \left( {\frac{t}{{10}} - \frac{x}{4}} \right) + \frac{\pi }{3}} \right]$. The wavelength of the wave is .... $m$
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(a) From the given equation $k = \frac{{2\pi }}{\lambda }$= Co-efficient of $x$
$ = \frac{\pi }{4}$ ==> $\lambda = 8\,m$
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The fundamental frequency of a sonometer wire increases by $6$ $Hz$ if its tension is increased by $44\%$ keeping the length constant. The change in the fundamental frequency of the sonometer wire in $Hz$ when the length of the wire is increased by $20\%$, keeping the original tension in the wire will be :-
The sound intensity level at a point $4 \,m$ from the point source is $10 \,dB$, then the sound level at a distance $2 \,m$ from the same source will be ........ $dB$
Statement$-1:$ Two longitudinal waves given by equations $y _{1}( x , t )=2 a \sin (\omega t - kx )$ and $y _{2}( x , t )= a \sin (2 \omega t -2 kx )$ will have equal intensity.
Statement$-2:$ Intensity of waves of given frequency in same medium is proportional to square of amplitude only.
A tuning fork gives $4$ beats with $50\, cm$ length of a sonometer wire if the length of the wire is shortened by $1\, cm$. the no. of beats still the same. The frequency of the fork is -............. $\mathrm{Hz}$
An organ pipe of length $L$ open at both ends is found to vibrate in its first harmonic when sounded with a tuning fork of $480\, Hz$. What should be the length of a pipe closed at one end, so that it also vibrates in its first harmonic with the same tuning fork ?
$41$ forks are so arranged that each produces $5$ beats per sec when sounded with its near fork. If the frequency of last fork is double the frequency of first fork, then the frequencies of the first and last fork are respectively
Two points are located at a distance of $10\; m$ and $15 \;m$ from the source of oscillation. The period of oscillation is $0.05 \;sec$ and the velocity of the wave is $300 \;m / s$. What is the phase difference between the oscillations of two points?
The phase difference between two waves, represented by ${y_1} = {10^{ - 6}}\sin \left\{ {100t + \left( {x/50} \right) + 0.5} \right\}\ m$ , ${y_2} = {10^{ - 6}}\cos \left\{ {100t + \left( {\frac{x}{{50}}} \right)} \right\}\ m$ where $x$ is expressed in metres and $t$ is expressed in seconds, is approximately .... $radians$