1. A wire of length 4.35 m and mass 137 g is under a tension of 125 N. What is the speed of a wave in this wire? If the tension is doubled, what is the speed? If the mass is doubled?

2. A wave on a string has the formula y = 0.030sin(0.55x - 62.8t). What is the wavelength, frequency, period, and speed of the wave. The string has a linear density μ = 0.020 kg/m. What is the tension in the string? What is the rate of energy flow of the wave?

3. On a point on a string, a peak of an harmonic wave is observed to pass every 0.050 s. The distance between peaks is 0.75 m. The height of the peak is 0.025 m. What is the equation of this wave? Assume that the wave is moving to the left. What is the speed of the wave? The string has a linear density μ = 0.020 kg/m. What is the tension in the string? What is the rate of energy flow of the wave?

4. The waves on a certain string move at 50.0 m/s. The string is 7.5 m long. If both ends are fixed, what are the first five resonance or standing wave frequencies? If one end is free, what are the first five frequencies? Is there any way of telling that a string is fixed or free at one end by looking at a sequence of resonance frequencies?
5. Sketch the superposition of the following wave pulses.
   

   

6. A wire of length 4.35 m and mass 137 g is under a tension of 125 N. A standing wave has formed which has seven nodes including the endpoints. What is the frequency of this wave? Which harmonic is it? What is the fundamental frequency? The maximum amplitude at the antinodes is 0.0075 m, write an equation for this standing wave.

7. A string fixed at one end only is vibrating in its ninth harmonic mode. Sketch the wave. The speed of a wave on the string is v = 25.8 m/s and the string has a length of 8.25 m. What is the frequency of the wave? What is the wavelength of the wave? What is the fundamental frequency?

8. Three successive resonance frequencies for a certain string are 175, 245, and 315 Hz. (a) Find the ratio of these three modes. (b) How can you tell that this sting has an antinode at one end? (c) What is the fundamental frequency? (d) Which harmonics are these resonance frequencies? (e) If the speed of transverse waves on this string is 125 m/s, find the length of the string?
9. While watching an archery show you recorded earlier, you notice that when the 1.05 m arrows hit a target they vibrate with the following pattern. Using frame advance on your PVR you deduce that the arrow vibrates 110 times per second. What is the speed of the waves travelling through the arrow?
   

   

Questions? mike.coombes@kwantlen.ca