Question

 

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?

Solution

Correct option is

648 N

 

Let λ be the wavelength, V the frequency and v the speed of each wave. Then  

           = coefficient of x in the argument of the sine function 

= coefficient of t in the argument of the sine function           

                = 120 π   

Which gives       V = 60 Hz.  

   

      

, where T is tension in the string.

SIMILAR QUESTIONS

Q1

A sonometer wire, 65 cm long, is in resonance with a tuning fork of frequency N. If the length of the wire is decreased by 1 cm and it is vibrated with the same tuning fork, 8 beats are heard per second. What is the value of N?

Q2

Two organ pipes, each closed at one end, give 5 beats per second when emitting their fundamental notes. If their lengths are in the ratio of 50 : 51, their fundamental frequencies (in Hz) are   

Q3

Two sources A and B are sounding notes of frequency 680 Hz. A listener moves from A to B with a constant velocity u. If the speed of sound is 340 ms –1, what must be the value of u so that he hears 10 beats per second?

Q4

A hospital uses an ultrasonic scanner of frequency 3.2 MHz to locate tumours in a tissue. What is the wavelength of ultrasonic waves in a tissue in which the speed of the waves is 1.6 km s–1 

Q5

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

Q6

 

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?

Q7

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? 

Q8

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

Q9

 

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 

Q10

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