The Fundamental Frequency Of A Longitudinal Vibrating Of A Rod Clamped At Its Centre Is 1500 Hz. If The Mass Of The Rod Is 96 G The Increase In Its Total Length Produced By A Stretching Force Of 10 Kg Weight Will Be:

Why Kaysons ?

Video lectures

Access over 500+ hours of video lectures 24*7, covering complete syllabus for JEE preparation.

Online Support

Practice over 30000+ questions starting from basic level to JEE advance level.

Live Doubt Clearing Session

Ask your doubts live everyday Join our live doubt clearing session conducted by our experts.

National Mock Tests

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

Organized Learning

Proper planning to complete syllabus is the key to get a decent rank in JEE.

Test Series/Daily assignments

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

SPEAK TO COUNSELLOR ? CLICK HERE

Question

The fundamental frequency of a longitudinal vibrating of a rod clamped at its centre is 1500 Hz. If the mass of the rod is 96 g the increase in its total length produced by a stretching force of 10 kg weight will be:

Solution

Correct option is

0.011 cm

 

The wavelength of waves in the rod = 2l (l = length of rod).

                    

Since the vibrations are longitudinal,

           

Since V = Al (where A is the area of c.s.)

If x is the increase in length produced by 10 kg weight, it follows:

        

from eq. (2) and (3),

        

Solving, we get x = 0.011 cm.

 

SIMILAR QUESTIONS

Q1

What is the ratio of the speed of sound in neon and water vapours at the same temperature? It is nearest to:

Q2

In case of the mechanical longitudinal wave y = A sin (ωt – kx) in air (density ρ), what is the relation between displacement amplitude and pressure amplitude?

Q3

A man beats a drum at a certain distance from a mountain. He slowly increases the rate of being and finds that the echo is not heard distinctly when the drum beating is at the rate of 40 per minute. He moves by 80 m towards the mountain and finds that the echo is again not heard distinctly when the rate of beating of the drum is 1 per second. What is the original distance of the man from the mountain?

Q4

In an experiment, it was found that a tuning fork and a sono-meter emitting its fundamental note, gave 5 beats per second both when the length of the wire was 1 metre and 1.05 metre. The velocity of transverse waves in the sono-meter wire is:

Q5

A slab of mass m is released from a height h0 from the top of a spring S’ of force constant  K. The maximum compression x of the spring is given by the equation:

                                                                           

Q6

A bob of mass m is oscillating as a simple pendulum with maximum amplitude θm. What is the maximum tension in the string?

Q7

A certain amount of acoustic energy is emitted in a uniform hemispherical pattern from a point source. At a distance of 5 m form the source the intensity is 5 W/m2. At a distance of 15 m the intensity will be:

Q8

 A 10 W source of sound of frequency 1000 Hz sends out waves in air. The displacement amplitude at a distance of 10 m from source will be: (Given velocity of sound = 350 m/s and density of air = 1.29 kg/m3)

Q9

The air in a closed tube 34 cm long is vibrating with 2 nodes and 2 antinodes and the temperature is 51oC. What is the wavelength of waves produced in air outside the tube when the temperature of air is 16oC?

Q10

If there are three sources of sound of equal intensity with frequencies 300, 301 and 302, the number of beats heard per second will be: