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- A copper wire has a density of =8920 kg/m3, a radius of 1.20 mm, and a length L. The wire is held under a tension of 10.00 N. Transverse waves are sent down the wire. (a) What is the linear mass density of the wire? (b) What is the speed of the waves through the wire?Four wave functions are given below. Rank them in order of the magnitude of the speeds, from least to greates t. y (x,1) = (0.10m) sin 2n x- 41+ I. I. y(x,t) = (0.10m) sin II. y (x.1) = (0.10m) sin +3) IV. y(x.1) = (0.10m) sin X- 41+ A. || = III, I - IV B. IV, II, III = | C. II, I, II, IV D. II, IV, II = | E. IV, II, ,Ithe wave function of a standing wave is given by A. 2Asin(kx)cos(wt) B. Asin(kx)cos(wt)
- 3T st+), find the -1 Consider a wave described by the wave function y (x,t)= 0.75m sin frequency of wave? O a. 4.67 Hz ОБ. 0.21 НZ O c. 0.51 Hz O d. 2.4 HzEx. 19 : The wave equation is represented by Y = 0.1 sin 4n quantities is in S.I. %3D 0.08 0.8 units, Calculate (1) wavelength and (2) Frequency.Which statement identifies a true relationship between the various wave components? O If amplitude increases, frequency increases. O If frequency increases, wavelength decreases. O If wavelength decreases, amplitude decreases.
- Write down w*w, for the following wave functions: a. W(x) = ekx b. W(x) = eAx с. Ф(x) %3D а + іx d. W(x) = cos(2TX)5 TE Consider a wave described by the wave function y (x,t)30.50m sin 9TT st+ 4. -1 ), find the 10 wavelength of wave? O a. 1.2 m O b. 0.89 m c. 1.12 m O d. 1.35 m DELLb) Consider the surface density wave 01 = σι 010e² (wt+40+ar³) " [4 marks] where t is time, the azimuthal angle, which increases clockwise, and r the radial coordi- nate. w is the angular frequency (w > 0), a is a positive constant. 10 is the amplitude of the wave. 1. Using mathematical arguments show whether the pattern described by σ ₁ is rotating clockwise or anticlockwise. [5 marks] 2. Using mathematical arguments show whether the pattern described by σ is a trailing or a leading spiral. [5 marks] 3. Consider now a point Po at a distance r = 5kpc from the centre C of the spiral. The point Po is at a peak of the surface density wave. Going outward from Po along the line passing through C and Po, and using a = (3kpc) determine the distance between C and the next peak of the surface density wave. -3 [5 marks]
- Consider the surface density wave 01 = 010e (w+30-ar³/4) where t is time, the azimuthal angle, which increases clockwise, and r the radial coordi- nate. w is the angular frequency (w > 0), a is a positive constant. 10 is the amplitude of the wave. 01 1. Using mathematical arguments show whether the pattern described by σ₁ is rotating clockwise or anticlockwise. 2. Using mathematical arguments show whether the pattern described by σ is a trailing or a leading spiral.9T s-1 + 4 Consider a wave described by the wave function y (x,t) =0.50m sin ( 3. 5TT -1 -m -), find the frequency of wave? in O a. 1.2 Hz O b. 1.125 Hz O c. 0.89 Hz O d. 1.35 Hz figure?5T 9T st+), find the 4 -1 TC Consider a wave described by the wave function y (x,t)%3D0.50m sin 3. 10 time period of wave? O a. 1.35 s O b. 1.12 s 1.2 s O d. 0.89 s A 34°C lt pilt hp