Physics 1100 In-Class Problems: Waves & Sound

1. A fisherman notices that his boat is moving up and down in a periodic way because of waves on the surface of the water. It takes 4.0 s for the boat to travel from its highest point to its lowest, a total distance of 3.0 m. The fisherman sees that the wave crests are spaced 8.0 m apart.
   (a) How fast are the waves moving?
   (b) What is the amplitude, frequency, wavelength, and period of the waves?
   

2. Radio waves travel at the speed of light, 3.00 × 10⁸ m/s. (a) AM radio waves have a frequency range of 530 kHz to 1600 kHz. What range of wavelengths does this correspond to? (b) FM waves have wavelengths of 2.77 m to 3.40 m. What range of frequencies does this correspond to?
   

3. Provided that the amplitude is high enough, the human ears can detect sound in the range of frequencies from about 20.0 Hz to about 20,000 Hz. Compute the wavelengths corresponding to the frequencies
   (a) for waves in air (v = 343 m/s);
   (b) for waves in water (v = 1480 m/s).
   

4. With what tension must a rope of length 5.00 m and mass 0.160 kg be stretched for transverse waves of frequency 60.0 Hz to have a wavelength of 0.800 m?
   

5. Transverse waves travel with a speed of 20.0 m/s in a string that is under a tension of 6.00 N. What tension is required for a wave speed of 30.0 m/s in the same string?
   

6. 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?
   

7. 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?
   

8. 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. Sketch the wave. What is the frequency of this wave? Which harmonic is it? What is the fundamental frequency?
   

9. 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 this wave? What is the wavelength of the wave? What is the fundamental frequency?
   

10. 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? Sketch each wave. (e) If the speed of transverse waves on this string is 125 m/s, find the length of the string?
    

Questions? mike.coombes@kwantlen.ca