Review: Chapter 16 Wave Motion
Q 1. A rope of mass 0.45 Kg is stretched between two supports 30 m apart. If the tension in the rope is 2400 N, how long does it take a pulse to travel from one support to the other ? (Ans: 0.075 s)
Q 2. The speed of a transverse wave propagating along a thin cylindrical copper wire is 200 m/s. Find the speed of such a wave along a second copper wire of half the diameter, assuming the tension is the same in both cases. (Ans: 400 m/s)
Q 3. At t = 0, a transverse wave pulse is a wire is described by the function
Y (X,0) = 8 / ( x2 + 111)
Where x and y are in cm. Calculate y at x = 3 and t = 1 s if the wave is traveling in the negative x direction with a speed of 4 m/s. (Ans: 0.05 m).
Q 4. A transverse wave in a string is described by
Y = 5.0 som (2 * x – 3 * t)
Where x and y are in cm and t in s. what is the magnitude of the transverse acceleration for the point located at x = 2 cm ?
Q 5. Consider a transverse wave in a long string described by
Y = 0.200 * sin (15 * x – 2 * PI * t + 3),
Where x and y are in cm and t is in s. what is the displacement of a point on the string at x = 2.5 cm and t = 3.51 s ? (Ans: 0.0785 cm)
Q 6. A traveling wave train on a string is harmonic, and its transverse displacement is given by y = 3.0 cos (PI * x – 4 * PI * t)
Where x and y are in cm and t is in s. Calculate the power required to generate these waves if the string has a length of 20 m and a mass of 50 g. Assume all the power produced by the source is delivered to the string. (Ans: 7.1 * 10(6))
Q 7. Harmonic wave 15 cm in amplitude are to be transmitted along a string that has a linear density of 4 * 102 Kg/m. if the maximum power delivered by the source is 500 W and the string is under a tension of 200 N, what is the highest vibrational frequency at which the source can operate ? (ans: 20 Hz)
Q 8. Two strings with linear densities mu1 and mu2 are joined together and are under the same tension. If a wave has a wavelength of 2.0 cm in string 1, what is the wavelength in string 2 ? (Ans: 2 * sqr (mu1/mu2)cm)
Q 9. Consider the following sinusoidal wave
Y (x,t ) = 10 cos (0.2 x – 100 t)
Where x,y are in cm and t is in s. At a given instant, let point A be at the origin 9x = 0 ) and point B be the first point along x that is 90 degrees out of phase with point A. What is the coordinate of point B ? (ans: 7.85 cm).