Worksheet: Production of Standing Waves

In this worksheet, we will practice determining the wavelength, frequency, and amplitude of standing waves produced through the superposition of traveling waves.

Q1:

Two sinusoidal waves with identical wavelengths and amplitudes travel in opposite directions along a string, producing a standing wave. The linear mass density of the string is 0.075 kg/m and the tension in the string is 5.0 N. The time interval between instances of total destructive interference is 0.13 s. What is the wavelength of the waves?

Q2:

A string is fixed at both ends to supports 3.50 m apart and has a linear mass density of 0.00500 kg/m. The string is under a tension of 90.00 N. A standing wave is produced on the string with six nodes and five antinodes.

Find the wave speed of the standing wave

Find the wavelength of the standing wave.

Find the frequency of the standing wave.

Find the period of the standing wave.

Q3:

A flute has a fundamental frequency of 262 Hz when air temperature is 35.0C. The flute is open at both ends. How long is the flute?

Q4:

Sound waves propagate through a tube that is open at both ends and has a length of 30 cm. The air temperature in the tube is 20C.

Find the wavelength of the sound waves.

Find the speed of the sound waves.

Find the frequency of the sound waves.

Q5:

A string, fixed on both ends, is 7.50 m long and has a mass of 0.130 kg. The string is under a tension of 112 N. The string is vibrating to produce a standing wave at the fundamental frequency of the string.

What is the speed of the waves on the string?

What is the wavelength of the standing wave produced?

What is the period of the standing wave produced?

Q6:

A standing wave is produced on a string by two sinusoidal transverse waves that are identical but moving in opposite directions. The string is fixed at 𝑥=0.00m and 𝑥=12.00m. Nodes appear at 𝑥=0.00m, 3.00 m, 6.00 m, 9.00 m, and 12.00 m. The amplitude of the standing wave is 2.50 cm. It takes 0.15 s for the antinodes to make one complete oscillation.

At the antinodes, what is the maximum speed of the string perpendicular to the direction of motion of the transverse waves?

  • A 5 2 4 𝜋 m/s
  • B 5 1 2 𝜋 m/s
  • C 3 2 𝜋 m/s
  • D 1 3 𝜋 m/s
  • E 2 3 𝜋 m/s

At the antinodes, what is the magnitude of the maximum acceleration of the string, perpendicular to the direction of motion of the transverse waves?

  • A 8 0 9 𝜋 m/s2
  • B 2 0 9 𝜋 m/s2
  • C 1 0 9 𝜋 m/s2
  • D 4 0 9 𝜋 m/s2
  • E 5 9 𝜋 m/s2

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