1. A sinusoidal wave is traveling along a string with a speed of 40 cm/s. The displacement of the particles of the string at x = 10.0 cm is found to vary with time according to the equation y(x,t) = 0.5 cm sin[1.0 - (4.0 s^-1) t]. The linear density of the string is 4.0 g/cm. What are a) the frequency and b) the wavelength of the wave? c) Write the general equation giving the transverse displacement of the particles of the string as a function of position. d) Calculate the tension of the string. 
   
2. Two sinusoidal waves, identical except for phase, travel in the same direction along a string and interfere to produce a resultant wave given by y’(x,t) = (3.0 mm) sin(20x -4.0t +0.820 rad), with x in meters and t in seconds. What are a) the wavelength l of the two waves, b) the phase difference between them and c) their amplitudes y_m. 
   
3. Two pulses travel along a string in opposite directions. The pulse that is traveling from right to left has gone through hard reflection at the boundary. The wave speed is 2.0 m/s and the pulses are 6.0 cm apart at t = 0 s. a) Sketch the pulses at t = 0, 10, 15, 20, 25 ms. b) What happens to the energy of the pulses at t = 15 ms? 
   
4. A string oscillates according to the equation y’(x,t) = (0.005 m) sin[(p/3) x] cos(40p t). a) What are the amplitude and the speed of the two waves? b) What is the distance between the nodes? c) What is the speed of the particle in the string at x = 1.5 cm and t = 9/8 s? 
   
5. A single pulse, whose wave shape is given by the function h (x-5t) is shown in the figure at t = 0 s. What are the a) speed, b) direction of the travel of the pulse? c) Plot h (x-5t) as a function of x for t = 2 s. d) Plot h(x-5t) as a function of t for x = 10cm.    
   
6. A sinusoidal wave traveling along a string is described by y (x, t) = 0.004 sin(72x -2.7t), in which the numerical constants are 0.004m, 72 rad/m and 2.7 rad/s. a) What is the amplitude of the wave? b) What are the wavelength, period and frequency of the wave? c) What is the speed of the wave? d) What is the displacement y at x = 22.5 cm and t =19s. e) What is the transverse speed of the element of the string? f) What is the transverse acceleration of the element of the string? 
   
7. a) Write an equation describing a sinusoidal transverse wave traveling on a cord in the +x direction with a wavelength of 10cm, a frequency of 400 Hz and amplitude of 2.0cm. b) What is the maximum speed of a point on the cord? c) What is the speed of the wave? 
   
8. A sinusoidal transverse wave is traveling along a string toward decreasing x. The plot shown in the figure is at t = 0s. The string tension is 3.6 N and its linear density is 25 g/m. Find a) the amplitude, b) the wavelength, c) the wave speed, and d) the period of the wave.  e) Find the maximum speed of the particle in the string? f) Write an equation describing the traveling wave.