Worksheet: Calculating Wave Motion

In this worksheet, we will practice using the wave speed formula, s = fλ, to calculate the movement of waves of different frequencies and wavelengths.

Q1:

Which of the following formulas correctly shows the relation between the frequency, the speed, and the wavelength πœ† of a wave?

  • A𝑠=𝑓+πœ†
  • B𝑠=π‘“βˆ’πœ†
  • C𝑠=π‘“πœ†
  • D𝑠=πœ†π‘“
  • E𝑠=π‘“πœ†

Q2:

A pier stretches from the coastline out into the sea a distance of 180 m. Waves on the sea move past the pier as they head toward the shore. The distance between the crests of the waves is 15 m, and the wave crests travel from the end of the pier to the shore in 24 seconds. What is the frequency of the waves?

Q3:

A sound wave in a particular object propagates at 960 m/s and has a frequency of 8,000 Hz. What is the wavelength of the sound wave in that object?

Q4:

A sound wave in a particular object propagates at 4,670 m/s and has a wavelength of 0.75 m. What is the frequency of the sound wave, to the nearest Hz?

Q5:

A sound wave in a particular object has a frequency of 260 Hz and a wavelength of 2.5 m. At what speed does the sound wave propagate in that object, to the nearest meter per second?

Q6:

A wave is shown in the diagram. What is the wavelength of the wave if its speed is 360 m/s?

Q7:

A wave is shown in the diagram. What is the frequency of the wave if its speed is 150 m/s?

Q8:

What is the frequency of the wave shown in the diagram?

Q9:

What is the frequency of the wave shown in the diagram?

Q10:

The speed of the wave shown in the diagram is 460 m/s.

What is the amplitude of the wave?

What is the wavelength of the wave?

What is the frequency of the wave?

At what value of distance is the wave’s positive displacement equal to its amplitude?

Q11:

A child jumps up and down in a large puddle and ripples of water spread out from around the child’s feet, as shown in the diagram. The time interval between the child’s landings in the puddle is 0.7 s, and the ripples are 65 cm apart. What is the speed of the waves that the child makes in the puddle?

Q12:

A vacationer standing on a jetty sees a plastic bottle floating in the sea bob up and down, as shown in the diagram. The time between the bottle being at its greatest height and returning to that height is 3 seconds. They also notice that the breaking waves pass the legs of the jetty nearest the shore and reach the shoreline in a time of 0.75 s. Assuming that the speed of the waves at the position of the bottle is the same as their speed between the jetty and the shore, what is the wavelength of the waves? Give your answer to one decimal place.

Q13:

Two waves, wave A and wave B, start to travel from points that intersect a line perpendicular to their direction of motion, as shown in the diagram. The waves travel through regions containing media with different properties. Both regions are the same size. Wave A has a wavelength of 1.5 m and a frequency of 50 Hz. Wave B has a wavelength of 2.5 m and a frequency of 20 Hz. Which of the following statements is correct?

  • AWave A and wave B reach the end of the region opposite to the end that they started from at the same time.
  • BWave A reaches the end of the region opposite to the end it started from before wave B does.
  • CWave A reaches the end of the region opposite to the end that it started from after wave B does.

Q14:

A wave moving through air has a frequency of 2,300 Hz and a wavelength of 0.15 m. A wave moving through water has a frequency of 750 Hz and a wavelength of 2 m.

Which wave travels at the greater speed?

  • AThe wave moving through water travels at the greater speed.
  • BThe wave moving through air travels at the greater speed.
  • CThe waves move at the same speed.

Which of the following statements about the periods of the wave motion of the two waves is correct?

  • AThe wave motion of the wave moving through the air has the longer period.
  • BThe wave motion of both waves has the same period.
  • CThe wave motion of the wave moving through water has the longer period.

Q15:

If 51 uniform water waves pass by a certain point in a lake in 3.4 s, what is the frequency of the waves?

  • A15 Hz
  • B50.6 Hz
  • C57.4 Hz
  • D173.4 Hz

Q16:

A sound source generates 90 oscillations each 3 seconds. Given that sound waves travel at 340 m/s in air, calculate the distance between the centres of a rarefaction and a successive compression.

  • A11.33 m
  • B5.67 m
  • C3.78 m
  • D2.83 m

Q17:

Calculate the value of 𝑋 given that the table shows the wavelength πœ† and the frequency 𝑓 of different waves, all having equal and constant speeds propagating in the same medium.

πœ† (m)10205𝑋2
𝑓 (Hz)603012040300
  • A25
  • B15
  • C13
  • D20

Q18:

A uniform oscillating wave is travelling in a stretched rope of length 20 m at a speed of 0.8 m/s. If 25 complete waves pass a certain point in 5 s, what is the number of complete waves across the whole length of the rope?

  • A5 waves
  • B625 waves
  • C3 waves
  • D125 waves

Q19:

Which of the following statements is correct regarding periodic motion?

  • AEvery periodic motion is a vibrational motion.
  • BEvery rotational motion is a periodic motion.
  • CEvery vibrational motion is a periodic motion.
  • DEvery periodic motion is a rotational motion.

Q20:

What is the range of wavelengths of sound a human ear can hear underwater, knowing that the range of frequencies a human ear can detect is from 20 Hz to 2Γ—10οŠͺ Hz and that the speed of sound underwater is 1,500 m/s?

  • A1.3 m to 13 m
  • B7.5 m to 75 m
  • C75 mm to 75 m
  • D13 mm to 13 m

Q21:

The ratio between the periodic time and the frequency of an oscillating object is 1238 s2. What is the number of oscillations which the object will complete in 35 seconds?

  • A630 oscillations
  • B416 oscillations
  • C540 oscillations
  • D729 oscillations

Q22:

A spring completes 4 complete oscillations in 5 seconds. What is its periodic time?

  • A1.25 seconds
  • B0.4 seconds
  • C1 second
  • D0.8 seconds

Q23:

A speaker generates sound waves which complete one vibration every 3 ms. Some person 170 metres away from the speaker hears the sound after 0.5 s from producing the sound. Calculate the distance between a compression and a successive rarefaction.

  • A0.26 m
  • B1.02 m
  • C0.51 m
  • D0.04 m

Q24:

A wave is propagating through space. If the distance between two successive points which have the same phase is 25 cm, then the wavelength is m.

  • A0.5
  • B0.25
  • C0.75
  • D1

Q25:

A mass is attached to a spring such that the spring has an equilibrium length of 11 cm. If a force is applied to the mass so the spring is compressed to 9 cm and then left to vibrate freely, what is the total distance covered by the mass after 3 complete vibrations?

  • A6 cm
  • B8 cm
  • C22 cm
  • D24 cm

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