I need help with part D, i and ii please :) A violin string of L-31.8 cm in length and u=0.64gm/linear mass density is tuned to play an A4note at 440.0 Hz. This means that the string is in its fundamental oscillation mode, i.e., it will be onthat note without placing any fingers on it. From this information,A. Calculate the tension on the string that allows it to be kept in tune.Given: The length of the violin string is 31.8 cm or 0.318 m.The linear mass density is 0.64 g/m or 0.64 x 10³ kg/m.The frequency is 440.0 Hz.To determine: (a) The tension in the stringFor the string fixed at both endsn²=Lwhere L is the length of the string and A is the wavelength.Rearrange the above equation for >λ =For the fundamental mode, n = 1λι = 2LThe speed isv=f₁2₁(1)where v is the speed of the wave on string, f, is the frequencySubstitute the value of λ, in equation (1)v = f₂2L(2)The expression for speed of the wave on string isV=(3)where T is the tensionFrom equation (2) and (3)=f,2LSquaring on both sides = f,2L²The tension from above equation isT = 4f²L²μSubstitute 0.64 x 103 kg/m for u, 440.0 Hz for f, and 0.318 m for L in the above equationT = 4 x 440 Hz³0.318 m² x 0.64 x 10³ kg/mT = 50.1 NThe tension in the string is 50.1 N.B. If from the midpoint of the string a maximum transverse motion 2.59 mm is observedwhen it is in the fundamental mode, what is the maximum speed vy máx of the string'santinode?(b) The maximum speed vy, maxThe maximum speed of the antinodeVy, max= Aw₁(4)where w₁ is the angular frequency and A is the amplitude of the wavew₁ = 2πf₁Substitute w, in equation (4)Vy, max= A2πf₁The amplitude is 2.59 mm or 0.00259 m.Vy, max= 0.00259 m X 2π X 440.0 Hzvy, max = 7.16 m/sThe maximum speed vy, max is 7.16 m/s.C. If the string tension is reduced by 6.3% of the tension found in A, what is the resultingfrequency of the note produced?(c) The resulting frequency when the string tension is reduced by 6.3 % of the tension found in AThe new tension in the string isT'T-6.3 IT¹ = 0.937 T100The frequency isf = ¹√2L0.937 Tf =2L √HSubstitute 0.64 x 103 kg/m for μ, and 0.318 m for L and 50.1 T for T in the above equationf=0.937x50.1 T= 425.8 Hz0.64 x 10 kg/m2x0.318 mThe resulting frequency when the string tension is reduced by 6.3 % of the tension found in A is 425.8 Hz. D. When playing violin different notes can be produced depending on the position of the fingers ofone hand on the string. The usual technique presses the string hard against the fingerboard,reducing the length of the string that can vibrate. If we consider this string initially tuned to an A4,and a finger is placed one third of the length down from the tuning peg:i. What would be the new fundamental frequency, i.e., the frequency of the new note beingproduced assuming the same tension as in A above?ii. What would be the new frequency of the note, if instead of using the technique describedabove for violin playing, the technique called artificial harmonic is used, where only partialpressure is put on the string so that it produces a knot on the string? Hint: the followingillustration may be useful to you.NutBridge12th Fret1/21/61/71/57th Fret1/35th Fret1/4Node

To determine: The new fundamental frequency The finger is placed one third of the length down from…

D. When playing violin different notes can be produced depending on the position of the fingers one hand on the string. The usual technique presses the string hard against the fingerboard, reducing the length of the string that can vibrate. If we consider this string initially tuned to an A4 and a finger is placed one third of the length down from the tuning peg: What would be the new fundamental frequency, i.e., the frequency of the new note being produced assuming the same tension as in A above? i. What would be the new frequency of the note, if instead of using the technique described above for violin playing, the technique called artificial harmonic is used, where only partial pressure is put on the string so that it produces a knot on the string? Hint: the following llustration may be useful to you.

D. When playing violin different notes can be produced depending on the position of the fingers one hand on the string. The usual technique presses the string hard against the fingerboard, reducing the length of the string that can vibrate. If we consider this string initially tuned to an A4 and a finger is placed one third of the length down from the tuning peg: What would be the new fundamental frequency, i.e., the frequency of the new note being produced assuming the same tension as in A above? i. What would be the new frequency of the note, if instead of using the technique described above for violin playing, the technique called artificial harmonic is used, where only partial pressure is put on the string so that it produces a knot on the string? Hint: the following llustration may be useful to you.