Worksheet: Modeling One-Dimensional Waves

In this worksheet, we will practice determining the change in the displacement of points on a wave along its propagation direction at different times.

Q1:

Which of the following formulas correctly relates the angular frequency πœ” of a wave to its frequency 𝑓 ?

  • A πœ” = πœ‹ 𝑓 
  • B πœ” = 2 πœ‹ 𝑓
  • C πœ” = 𝑓 2 πœ‹
  • D πœ” = 2 πœ‹ 𝑓
  • E πœ” = 𝑓 πœ‹ 2

Q2:

Which of the following formulas correctly relates the displacement of a point on a wave 𝑠 to the distance π‘₯ from the source of the wave, the time 𝑑 that the wave has been generated for, the amplitude 𝐴 of the wave, the wave number π‘˜ of the wave, and the wave’s angular frequency πœ” ?

  • A 𝑠 = 𝐴 ( π‘˜ 𝑑 βˆ’ πœ” π‘₯ ) s i n
  • B 𝑠 = 𝐴 ( π‘˜ π‘₯ βˆ’ πœ” 𝑑 ) s i n
  • C 𝑠 = 𝐴 ( π‘˜ πœ” βˆ’ π‘₯ 𝑑 ) s i n
  • D 𝑠 = 𝐴 ( πœ” βˆ’ π‘˜ π‘₯ 𝑑 ) s i n
  • E 𝑠 = 𝐴 ( π‘₯ 𝑑 βˆ’ π‘˜ πœ” ) s i n

Q3:

A wave with a wavelength πœ† propagates through a distance π‘₯ . Which of the following formulas correctly represents the number of wavelengths that the wave propagates through?

  • A π‘₯ πœ†
  • B ( π‘₯ + πœ† ) ( π‘₯ – πœ† )
  • C π‘₯ πœ†
  • D ( π‘₯ βˆ’ πœ† ) ( π‘₯ + πœ† )
  • E πœ† π‘₯

Q4:

Which of the following formulas correctly relates the displacement of a point on a wave, 𝑠 , to the distance, π‘₯ , from the source of the wave, the time, 𝑑 , that the wave has been generated for, the amplitude, 𝐴 , of the wave, the frequency, 𝑓 , of the wave, and its wavelength, πœ† ?

  • A 𝑠 = 𝐴 ( 2 πœ‹ ( π‘₯ πœ† – 𝑓 𝑑 ) ) s i n
  • B 𝑠 = 𝐴 ο€½ 2 πœ‹ ο€½ π‘₯ πœ† – 𝑓 𝑑   s i n
  • C 𝑠 = 𝐴 ο€» 2 πœ‹ ο€» π‘₯ πœ† – 𝑓 𝑑   s i n
  • D 𝑠 = 𝐴 ο€½ 2 πœ‹ ο€½ π‘₯ πœ† – 𝑓 𝑑   s i n
  • E 𝑠 = 𝐴 ο€½ 2 πœ‹ ο€½ π‘₯ πœ† – 1 𝑓 𝑑   s i n

Q5:

Which of the following formulas correctly relates the wave number, π‘˜ , of a wave to its wavelength, πœ† ?

  • A π‘˜ = 2 πœ† πœ‹
  • B π‘˜ = 2 πœ‹ πœ†
  • C π‘˜ = πœ‹ πœ† 2
  • D π‘˜ = πœ† 2 πœ‹
  • E π‘˜ = 2 πœ‹ πœ†

Q6:

A wave has a period 𝑇 . Which of the following formulas correctly represents the number of complete oscillations that will pass through a certain point in a time 𝑑 ?

  • A 𝑑 𝑇
  • B 𝑇 𝑑
  • C ( 𝑇 βˆ’ 𝑑 ) ( 𝑇 + 𝑑 )
  • D ( 𝑇 + 𝑑 ) ( 𝑇 – 𝑑 )
  • E 𝑇 𝑑

Q7:

A wave is generated at a point 𝑃 . The wave has a wavelength of 2.5 m and a frequency of 160 Hz. At an instant 𝑑 s e c o n d s after the wave starts to propagate, it has moved 2.8 m away from 𝑃 . What is the time interval between the wave starting to propagate and it having propagated a distance of 2.8 m?

Q8:

The following diagrams, diagram (a) and diagram (b), show the changes in the displacement of two waves.

In each diagram, the graph with the black curve shows the change in the displacement of a wave with time at a fixed distance from the source of the wave, and the graph with the blue curve shows the change in the displacement of the wave with distance from the source of the wave at a fixed time. The graphs for both waves have the same displacement, distance, and time scale as each other.

The displacement–distance graphs for both waves measure distance from the same point and at the same instant, and the displacement–time graphs for both waves measure time from the same instant and at the source of each wave. Both waves have an initial displacement of zero, and both initially increase their positive displacements.

Which of the following statements correctly describes the difference between the wave represented by diagram (a) and the wave represented by diagram (b)?

  • ABoth waves have the same amplitude and frequency. The sources of both waves have the same position and both waves start to be generated at the same time. The waves have different initial phases.
  • BIn both diagrams, the waves have the same rate of change of displacement with time, but the sources of the waves do not begin to be generated at the same time.
  • CIn both diagrams, the waves have the same rate of change of displacement with distance from the sources of the waves, but the sources of the waves are not at the same position.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.