Question

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?

Solution

Correct option is

 

Mass of the wire (M) = 30 g = 30 × 10 –3 kg. Mass per unit length of the wire (m) = 4 × 10 –2 kg m–1.   

Therefore, length of the wire is   

                        

Now, for the fundamental mode,  Therefore,

                        

SIMILAR QUESTIONS

Q1

A bat flying above a take emits ultrasonic sound of 100 kHz. When this wave falls on the water surface, it is partly reflected and partly transmitted. What are the wavelengths of the reflected and transmitted waves? The speed of sound in air is 340 ms –1 and in water 1450 ms–1

Q2

 

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?

Q3

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? 

Q4

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

Q5

 

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 

Q6

 

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?

Q7

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

Q8

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.

Q9

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 

Q10

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