A metallic rod of length 1m is rigidly clamped at its mid point. Longirudinal stationary wave are setup in the rod in such a way that there are two nodes on either side of the midpoint. The amplitude of an antinode is `2 xx 10^(-6) m`. Write the equation of motion of a point 2 cm from the midpoint and those of the constituent waves in the rod, (Young,s modulus of the material of the rod `= 2 xx 10^(11) Nm^(-2)` , density `= 8000 kg-m^(-3)`). Both ends are free.

A metallic rod of length 1m is rigidly clamped at its end points. Longitudinal stationary waves are setup in the ord in such a way that there six antinodes of displacement wave observed along the rod. The amplitude of the anotinode is 2 xx 10^(-6) m . Write the equations of the stationary wave and the component waves at the point 0.1 m from the one end of the rod. [Young modulus = 7.5 xx 10^(10)N//m^(2) , density = 2500 kg//m^(3) ]

If the young's modulus of the material of the rod is 2 xx 10^(11) N//m^(2) and its density is 8000 kg//m^(3) then the time taken by a sound wave to traverse 1m of the rod will be

A metallic rod of length 1m has one end free and other end rigidly clamped. Longitudinal stationary waves are set up in the rod in such a way that there are total six antinodes present along the rod. The amplitude of an antinode is 4 xx 10^(-6) m . young's modulus and density of the rod are 6.4 xx 10^(10) N//m^(2) and 4 xx 10^(3) Kg//m^(3) respectively. Consider the free end to be at origin and at t=0 particles at free end are at positive extreme. The magnitude of strain at midpoint of the rod at t = 1 sec is

A metallic rod of length 1m has one end free and other end rigidly clamped. Longitudinal stationary waves are set up in the rod in such a way that there are total six antinodes present along the rod. The amplitude of an antinode is 4 xx 10^(-6) m . young's modulus and density of the rod are 6.4 xx 10^(10) N//m^(2) and 4 xx 10^(3) Kg//m^(3) respectively. Consider the free end to be at origin and at t=0 particles at free end are at positive extreme. The equation describing stress developed in the rod is

A metallic rod of length 1m has one end free and other end rigidly clamped. Longitudinal stationary waves are set up in the rod in such a way that there are total six antinodes present along the rod. The amplitude of an antinode is 4 xx 10^(-6) m . young's modulus and density of the rod are 6.4 xx 10^(10) N//m^(2) and 4 xx 10^(3) Kg//m^(3) respectively. Consider the free end to be at origin and at t=0 particles at free end are at positive extreme. The equation describing displacements of particles about their mean positions is.

A metallic rod of length 1 m, young's modulus 3xx10^(11)Nm^(-3) and density is clamped at its middle. Longitudinal stationary vibrations are produced in the rod with the total number of displacement nodes equal to 3. The frequency of vibrations is

A steel rod 100 cm long is clamped at its midpoint. The fundamental frequency of longitudinal vibrtions of the rod is 3 kHz. What is the speed of the sound in the rod?

The length of a rod is 5 xx 10^(2) m , the order of magnitude of the length of the rod is

A copper rod of length 1.0 m is clamped at its middle point. Find the frequencies between 20 Hz and 20,000 Hz at which standing longitudinal waves can be set up in the rod. The speed of sound in copper is 3.8 km s^-1 .