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Waves Practice Questions

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Updated on Sep 27, 2011

Review these concepts at: Waves Study Guide

Practice Questions

  1. The speed of a radio wave is 3 · 105 km/s and the frequency is 104 Hz. Find the wavelength and the period of the wave.
  2. A particle on the surface of a string acted on by a transversal wave repeats 10 cycles in 6 seconds. The wave propagates at a rate of 10 cm/s. Find the frequency and speed of the wave.
  3. If two musical cords are acted on by the same force, but at the same length, one is two times heavier than the other, how do the speeds of the waves in the two cords compare?
  1. Sound travels with a speed of 343 m/s in air. Find the speed of sound in steel where K = 200 GPa and ρ = 7,870 kg/m3, and in water where E = 2,200 GPa and ρ = 1,000 kg/m3. Compare to the speed in air.
  2. The same source is used to propagate sound between two points. Two different materials are tested to find one that can achieve greater speed. At the same modulus of elasticity, which material will perform better: the lower density or the higher density one? Explain
  3. Based on the answer in practice problem 4, what is your expectation for the speed of sound in ice, water, and steam: increase, decrease, stay the same? Explain.
  4. When sound travels in between two different media, the frequency remains the same. What happens to the wavelength of a sound that travels from air to water?
  1. Ultraviolet waves of 5 · 10-–8 m are produced by the sun. What is the frequency of the waves? What is the time for the waves to travel to Earth? The distance to the sun is 1.5 · 1011 m.
  2. For best performance, an antenna has to have a length half of the wavelength of the received wave. Find the size of an antenna that receives frequencies of 108 Hz.
  3. A wave is propagating through a vacuum, and the amplitude of the electric field is 200 V/m. Find the energy of the wave and the amplitude of the magnetic field necessary to propagate this wave.

Answers

  1. λ = V/f = 3 · 104 m and the period is T = l/f = 10–4s
  2. f = 10 cycles/6 s = 1.7 Hz, T = l/f = 0.6 s, v = 10 cm/s = 0.1 m/s
  3. vheavy/vlight= (1/2) < 1 hence vheavy < vlight
  4. 5,040 m/s in steel and 4.7 · 104 m/s in air; both much larger than the speed of sound in air
  5. v is proportional to p1/2 s° with increasing density the speed decreases.
  6. Both ice and steam have – 1/2 lower density than liquid water, hence the speed will be smaller in water, but larger in ice and steam.
  7. Because vice is larger than vwater and at constant frequency speed is proportional to wavelength then λice > λwater
  8. The time of travel is t = d/c = 500 s and the frequency of the waves is: f = c / λ = 6 · 1015 Hz
  9. L = λ/2 = v/ 2 · f = 1.5 m
  10. E = c · B hence the magnetic field will be B = E / c = 6 · 10–5 T and the energy is u = B20 = 3 · 10–7J
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