Question

A steel rod of length 1.0 m is clamped rigidly at its middle. What is the frequency of the fundamental mode for the longitudinal vibrations of the rod? The speed of sound in steel = 5 × 103 ms –1 

Solution

Correct option is

2.5 kHz

 

Since the rod is clamped rigidly in the middle, the middle point of the rod is a node. In the fundamental mode, the end-points of the rod are antinodes. Therefore, the distance between two consecutive antinodes = L= 1.0 m. But, the distance between two consecutive antinodes is λ/2.   

 The frequency of the fundamental mode is  

               

SIMILAR QUESTIONS

Q1

 

The particle displacements in a travelling harmonic wave are given by 

                

Where x and y are in centimeters and t is in seconds. What is the phase difference between oscillatory motion at two points separated by a distance of 4 m?

Q2

A string of length 10.0 m and mass 1.25 kg is stretched with a tension of 50 N. If a transverse pulse is created at one end of the string, how long does it take to reach the other end? 

Q3

A uniform metal wire of density ρ, cross-sectional area A and length L is stretched with a tension T. The speed of transverse wave in the wire is given by

Q4

 

Standing waves are produced by the superposition of two waves

                     

and             

Where x and y are expressed in metres and t is in seconds. What is the amplitude of a particle at x = 0.5 m. Given 

Q5

 

The transverse displacement of a string fixed at both ends is given by 

                            

Where x and y are in metres and t is in seconds. The length of the string is 1.5 m and its mass is 3.0 × 10–2 kg. What is the tension in the string?

Q6

A wire of density ρ is stretched between two clamps a distance L apart, while being subjected to an extension lY is the Young’s modulus of the material of the wire. The lowest frequency of transverse vibrations of the wire is given by

Q7

A pipe of length 20 cm is closed at one end. Which harmonic mode of the pipe is resonantly excited by a 425 Hz source? The speed of sound = 340 ms –1.

Q8

A pipe of length 20 cm is open at both ends. Which harmonic mode of the pipe is resonantly excited by a 1700 Hz source? The speed of sound = 340 ms–1 

Q9

A wire has a mass 30 g and linear density 4 × 10 –2 kg m–1. It is stretched between two rigid supports and vibrates in its fundamental mode with a frequency of 50 Hz. What is the speed of transverse waves on the wire?

Q10

Two tuning forks A and B produce 10 beats per second when sounded together. On slightly loading fork A with a little wax, it was observed that 15 beats are heard per second. If the frequency of fork B is 480 Hz, what is the frequency of fork A before it was loaded?