Question

A sonometer wire of length 120 cm is divided into three segments of lengths in the ratio of 1 : 2 : 3. What is the ratio of their fundamental frequencies?

Solution

Correct option is

6 : 3 : 2

 

The frequency of the fundamental mode is given by

                                 

Now L1 = 20 cm, L2 = 40 cm and L3 = 60cm. Therefore

                

SIMILAR QUESTIONS

Q1

Figure shows three identical springs A, B, C. When a 4 kg weight is hung on A, it descends by 1 cm. When a 6 kg weight is hung on C, it will descent by

                                                   

Q2

A spring of force constant k is cut into two equal halves. The force constant of each half is

Q3

Two springs of equal lengths and equal cross-sectional areas are made of materials whose Young’s modulii are in the ratio of 3:2. They suspended and loaded with the same mass. When stretched and released, they will oscillate with time periods in the ratio of

Q4

Two bodies A and B of equal masses are suspended from two separate springs of force constants k1 and k2 respectively. If the two bodies oscillate such that their maximum velocities are equal, the ratio of the amplitudes of oscillation of A and B will be

Q5

Two springs A and B have force constants k1 and k2 respectively. The ratio of the work done on A to that done on B in increasing their lengths by the same amount is

Q6

Two springs A and B have force constants k1 and k2 respectively. The ratio of the work done on A to that done on B when they are stretched by the same force is

Q7

The mass m shown in figure is displaced vertically by a small amount and released. If the system oscillates with a period of 2 seconds, the value of the spring constant k is

                                                              

Q8

A spring of force constant k is cut into three equal pieces. If these three pieces are connected in parallel, the force constant of the combination will be

Q9

Two springs of force constants k1 and k2 are connected as shown in figure. The time period of vertical oscillations of mass m is given by

                                                                

Q10

A particle is in linear simple harmonic motion between two extreme pointsA and B, 10 cm apart (see fig). If the direction from A to B is taken as positive direction, what are signs of displacement x, velocity V and acceleration a, when the particle is at A