Plz solve this numerical

Plz solve this numerical (8) A uniform wire under tension, is fixed at its ends. If the ratio of tension in the wire to the square of its length is 360 dyne/cm and fundamental frequency of vibration of wire is 300 Hz, find its linear density. (Ans: 10-4 kg/m) (9) A wire is in unison with a fork of frequency 250 HI, when stretched by a weight hanging vertically. On immersing the weight in water, the wire produces ten beats per second with the same fork. Calculate density of material of weight, if density of water is one g per cc. (Ans : 12.76 g/cc) (10) Two simple harmonic proéressive waves are represented by Y 1 2 sin 2Tt 100t— — cm. The waves and 2 sin 2n 100t+ — combine to form a stationary wave. Find (i) amplitude at antinode (ii) distance between adjacent node and adjacent antinode. (iii) loop length fiv) wave velocity. (Ans: 4 cm, 15 cry, 30 cm. 60 m/s) (II) The equation of a sånding wave is given by Y = 0.02 (100 at) m . Find the interfering, amplitude of either wave waveLgpgth, time period, frequency and wave velocity of interfering waves. (Ans : o.m 2 m. 0.02 s, so Hz 200 (12) In Melde's experiment, find weight added in the pan when number of loops on the string changes from 4 to 2, if initial tension on the string is 1960 dyne and mass of the pan is one gram. (Ans: 7g wt) (13) (14) (15) In Melde's experiment, tuning fork was arranged in parallel position and 6 loops were formed along a length of 7.2 m of the string stretched by a weight of log. If mass of the string is 14.4 x 10-2 g, find the frequency of tuning fork. (Ans : 58.33 H,) Find the frequency of fifth overtone of an air column vibrating in a pipe closed at one end. Length of pipe is 42.10 cm long and speed of sound in air at room temperature is 350 ml.s. (Inner diameter of pipe is 3.5 cm) : 2231 H,) Two organ pipes. open at both ends, are sounded together and 5 heats are heard per second. The length of shorter pipe is O.ås m. Find the length of the other pipe. (Given: velocity of sound in air 350m/s and end correction at one end 0.015 m, same for both pipes) (16) The fundamental frequency of a pipe closed at one end is in unison with the third overtone of an open pipe. Calculate the ratio of their lengths of air column. (17) Show that for pipe open at both ends, the end correction is e = where the symbols have their usual meanings. (18) In a resonance tube experiment, a tuning fork resonates with an air column IOcm long and agam resonates when it is 32.2cm long. Calculate the wavelength of wave and the end correction. (Ans :