A musical instrument is made using four different metal strings, 1, 2, 3 and 4 with mass per unit length $$\mu $$, 2$$\mu $$, 3$$\mu $$ and 4$$\mu $$ respectively. The instrument is played by vibrating the strings by varying the free length in between the range L₀ and 2L₀. It is found that in string-1$$\mu $$ at free length L₀ and tension T₀ the fundamental mode frequency is f₀.

List-I gives the above four strings while list-II lists the magnitude of some quantity.



The length of the strings 1, 2, 3 and 4 are kept fixed at L₀, $${{3{L_0}} \over 2}$$, $${{5{L_0}} \over 4}$$ and $${{7{L_0}} \over 4}$$ respectively. Strings 1, 2, 3 and 4 are vibrated at their 1st, 3rd, 5th and 14th harmonies, respectively such that all the strings have same frequency.

The correct match for the tension in the four strings in the units of T₀ will be

A student is performing the experiment of resonance Column. The diameter of the column tube is 4 cm. The frequency of the tuning fork is 512 Hz. The air temperature is 38^oC in which the speed of sound is 336 m/s. The zero of the meter scale coincides with the top end of the Resonance Column tube. When the first resonance occurs, the reading of the water level in the column is

A police car with a siren of frequency 8 kHz is moving with uniform velocity 36 km/hr towards a tall building which reflects the sound waves. The speed of sound in air is 320 m/s. The frequency of the siren heard by the car driver is

Column I shows four systems, each of the same length L, for producing standing waves. The lowest possible natural frequency of a system is called its fundamental frequency, whose wavelength is denoted as $$\lambda$$_f. Match each system with statements given in Column II describing the nature and wavelength of the standing waves :