A string fixed at both ends resonates at a certain fundamental frequency. Which of the following adjustments would not affect the fundamental frequency?
Tension is made four times and length is doubled
Tension is doubled and length is halved
Both tension and length are halved
Both length and tension are doubled
A piano string $1.5\,m$ long is made of steel of density $7.7 \times 10^3 \,kg/m^3$ and Young’s modulus $2 \times 10^{11} \,N/m^2$. It is maintained at a tension which produces an elastic strain of $1\%$ in the string. The fundamental frequency of transverse vibrations of string is ......... $Hz$
A wire of density $9 \times 10^3 \,kg/m^3$ is stretched between two clamps one meter apart and is subjected to an extension of $4.9 \times 10^{-4} \,m$. What will be the lowest frequency of the transverse vibrations in the wire ... $Hz$ $[Y = 9 \times 10^{10} \,N/m^2]$ ?
Two uniform strings $A$ and $B$ made of steel are made to vibrate under the same tension. if the first overtone of $ A$ is equal to the second overtone of $B$ and if the radius of $A$ is twice that of $B,$ the ratio of the lengths of the strings is
A string of length $1\ m$ fixed at both ends is vibrating in $3^{rd}$ overtone. Tension in string is $200\ N$ and linear mass density is $5\ gm/m$ . Frequency of these vibrations is ..... $Hz$
A string is rigidly tied at two ends and its equation of vibration is given by $y = \cos 2\pi \,t\sin \sin \pi x.$ Then minimum length of string is .... $m$