QUICK QUIZ 16.1 (end of section 16.2) While sitting at the beach, you count the number of waves that hit the beach during a certain amount of time. This measurement is most closely associated with a) the period of the waves, b) the frequency of the waves, c) the wavelength of the waves, or d) the speed of the waves.
QUICK QUIZ 16.1 ANSWER (b). The frequency of a wave is associated with the number of cycles of the wave that occur in a given amount of time. When we count the waves that hit the beach, we are actually counting the number of wave crests.
QUICK QUIZ 16.2 (end of section 16.2) In Equation 16.10, y = A sin(kx – wt), for a traveling sinusoidal wave, the variable, k, is related to the spring constant, k, from Chapter 15 a) in the sense that it is related to a force, b) in the sense that it is associated with a displacement, c) in the sense that it is associated with oscillatory motion, or d) is not related to the spring constant, k.
QUICK QUIZ 16.2 ANSWER (d). Unfortunately, when representing the large quantity of physical variables that exist, the alphabet becomes quickly exhausted. The variable k is used for two completely different quantities, the spring constant and the wave number. These quantities must be completely different since the units are completely different.
QUICK QUIZ 16.3 (end of section 16.3) You suspend an object from the end of a hanging rubber band, send a pulse along the band and measure the speed of the pulse to be v. You then quadruple the mass of the object that you hang on the rubber band and the rubber band’s length increases by a factor of two from its original length with the first object. If you now send a pulse along the band, the speed of the pulse will be a) v/(22) b) v/2, c) v/2, d) v, e) 2 v, f) 2v, or g) (22)v
QUICK QUIZ 16.3 ANSWER (g). By increasing the mass of the hanging object by a factor of four, you have increased the tension by a factor of four. Since the rubber band has doubled its length, its mass per unit length or linear mass density has gone down by a factor of two. Therefore,
QUICK QUIZ 16.4 (end of section 16.5) You perform an experiment on a string and generate sinusoidal waves of an amplitude, A, and frequency, f. You then perform a similar experiment on a string that has twice the linear mass density and which is under half the tension as the original string. To generate sinusoidal waves of an amplitude, A, and frequency, f, in this new string, you will have to transfer energy to the new string at a rate that is a) one fourth the rate for the original string, b) half the rate for the original string, c) the same as the rate for the original string, d) twice the rate for the original string, or e) four times the rate for the original string.
QUICK QUIZ 16.4 ANSWER (c). Equation 16.21 relates the energy rate transfer to the linear mass density, frequency, amplitude and speed. The speed is in turn related to the tension and the linear mass density so that the equation may be rewritten, Therefore, if one doubles the linear mass density and halves the tension, the rate of energy transfer must remain the same to keep the same amplitude and frequency.
QUICK QUIZ 16.5 (end of section 16.6) Which of the following is a solution to the linear wave equation? a) y = x + vt2, b) y = sin2(x + vt), c) both a and b, d) neither a nor b.
QUICK QUIZ 16.5 ANSWER (b). Only functions of the form y = f(x ± vt) are solutions to the wave equation. The function y = x + vt2 is not of this form and it is easy to verify that it is not a solution. We have, Since 0 is not, in general, equal to 2/v, the function is not a solution to the wave equation. On the other hand, y = sin2(x + vt) is of the form y = f (x ± vt) and is a solution to the wave equation. We have,