The string of a violin has a frequency of $440 \,cps$. If the violin string is shortened by one fifth,its frequency will be changed to ........... $cps$.

The equation of vibration of a stretched string fixed at both ends and vibrating in $5^{\text{th}}$ harmonic is $Y = 3 \sin(0.4x) \cos(200\pi t)$, where '$x$' and '$Y$' are in $cm$ and '$t$' is in seconds. The length of the string is: (in $\pi \text{ cm}$)

The frequency of a sonometer wire is $f$. When the weights producing the tension are completely immersed in water,the frequency becomes $f/2$. When the weights are immersed in a certain liquid,the frequency becomes $f/3$. The specific gravity of the liquid is:

The total length of a sonometer wire between fixed ends is $110 \ cm$. Two bridges are placed to divide the length of the wire in the ratio $6 : 3 : 2$. The tension in the wire is $400 \ N$ and the mass per unit length is $0.01 \ kg/m$. What is the minimum common frequency with which the three parts can vibrate in $Hz$?

$A$ 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 number of beats is still the same. The frequency of the fork is (in $Hz$)

The fundamental frequency of a sonometer wire is $n$. If the tension is increased $3$ times,the length is increased $3$ times,and the diameter is increased $2$ times,what will be the new frequency?