$A$ wire vibrates at a fundamental frequency of $500 \,Hz$. $A$ second identical wire produces $5$ beats per second with it when the tension in the first wire is slightly decreased. The ratio of the tension in the second wire to the tension in the first wire is approximately equal to

The number of beats produced per second by two vibrations: $x_1 = x_0 \sin(646\pi t)$ and $x_2 = x_0 \sin(652\pi t)$ is

The frequencies of two sound sources are $256 \text{ Hz}$ and $260 \text{ Hz}$. At $t = 0$,the intensity of sound is maximum. Then the phase difference at the time $t = \frac{1}{16} \text{ s}$ will be

Beats are produced by two waves given by $y_{1} = a \sin(2000 \pi t)$ and $y_{2} = a \sin(2008 \pi t)$. The number of beats heard per second is

When two tuning forks (fork $1$ and fork $2$) are sounded simultaneously,$4$ beats per second are heard. Now,some tape is attached to the prong of fork $2$. When the tuning forks are sounded again,$6$ beats per second are heard. If the frequency of fork $1$ is $200 \, Hz$,then what was the original frequency of fork $2$ (in $, Hz$)?

Three sound waves of equal amplitudes have frequencies $(n - 1)$,$n$,and $(n + 1)$. They superimpose to produce beats. The number of beats produced per second is: