Question

The length of a sonometer wire AB is 100 cm. Where should the two bridges be placed from end A to divide the wire in three segments whose fundamental frequencies are the ratio of 1:2:3?

Solution

Correct option is

60 cm, 90 cm

For a wire,  Therefore, frequencies will be in the ratio of 1:2:3 if lengths are in the ratio of  the lengths are in the ratio of 6:3:1. Total length = 100 cm. Therefore L1 = 60 cm, L2 = 30 cm and L1 = 10 cm.

SIMILAR QUESTIONS

Q1

An organ pipe P1, closed at one end vibrating in its first harmonic and another pipe P2, open at both ends vibrating in its third harmonic, are in resonance with a given tuning fork. The ratio of the lengths of P1 and P2is

Q2

Two identical straight wires are stretched so to produce 6 beats per second when vibrating simultaneously. On changing the tension slightly in one of them, the beat frequency remains unchanged. Denoting by T1 andT2 the higher and the lower initial tensions in the strings, then it could be said that while making the above changes in tension.

Q3

The time taken by a particle executing simple harmonic motion of time period T to move from the mean position to half the maximum displacement is

Q4

To raise the pitch of a stringed musical instrument, the player can

Q5

One end a long metallic wire of length L is tied to the ceiling. The other end is tied to a massless spring of spring constant K. A mass m hangs freely from the free end of the spring. The area of cross-section and Young’s modulus of the wire are A and Y respectively. If the mass is slightly pulled down and released, it will oscillate with a time period given by

Q6

A weight is attached to the free end of a sonometer wire. Resonance occurs at a length of 40 cm of the wire with a tuning fork of frequency 512 Hz. The weight is then immersed wholly in water, the resonant length is reduced to 30 cm. The relative density of the weight is

Q7

A particle is executing simple harmonic motion along the x-axis with amplitude 4 cm and time period 1.2 s. The minimum time taken by the particle to move from x = +2 cm to x = +4 cm and back again is

Q8

 

Two waves are represented by the following equations:

                   

The ratio of intensities I2/I1 will be

Q9

The velocity of sound in a diatomic gas is 300 ms–1. What is the rms velocity of its molecules?  

Q10

A toothed wheel is rotated at 120 r.p.m. A post card is placed against the teeth. How many teeth must the wheel have to produce a note whose pitch is the same as that of a tuning fork of frequency 256 Hz?