4.5 Standing Waves

Which of the following best describes a standing wave?

A. A wave that travels in one direction only

B. A wave that is formed by the superposition of two waves travelling in opposite directions

C. A wave that does not have any nodes or antinodes

D. A wave that always has a constant frequency and amplitude

In a standing wave, what is the phase difference between particles at a node and an antinode?

A. 0 degrees

B. 90 degrees

C. 180 degrees

D. 360 degrees

Which of the following is NOT a characteristic of nodes in a standing wave?

A. Maximum amplitude

B. No displacement

C. Points of destructive interference

D. Remain stationary

How are antinodes formed in a standing wave?

A. By destructive interference of two waves

B. Where the amplitude of the wave is zero

C. By constructive interference of two waves

D. Where the wave speed is maximum

If the distance between two consecutive nodes in a standing wave is 25 cm, what is the wavelength of the wave?

A. 25 cm

B. 50 cm

C. 75 cm

D. 100 cm

a) Explain how standing waves are formed when two waves of the same frequency and amplitude travel in opposite directions in a medium. [3]

b) A string of length 1.2 m is fixed at both ends and is made to vibrate in its second harmonic. Calculate the wavelength of the standing wave formed. [2]

a) Define the terms 'node' and 'antinode' in the context of standing waves. [2]

b) A pipe open at both ends produces a standing wave with a frequency of 440 Hz. If the speed of sound in air is 340 m/s, determine the length of the pipe. [3]

a) Describe the difference in the formation of standing waves in a pipe that is closed at one end compared to a pipe that is open at both ends. [3]

b) A pipe closed at one end has a length of 0.5 m. If the speed of sound in air is 340 m/s, calculate the fundamental frequency of the standing wave produced in the pipe. [2]

a) How does the length of a pipe affect the frequency of the standing wave produced when it is closed at one end? [2]

b) A pipe closed at one end has a length of 0.75 m. If the speed of sound in air is 340 m/s, calculate the first three harmonics of the standing wave produced in the pipe. [4]

c) Explain why a pipe closed at one end does not produce even harmonics. [2]

a) Describe the difference between the first and second harmonics in a pipe that is open at both ends. [3]

b) If the second harmonic in a pipe open at both ends has a frequency of 256 Hz and the speed of sound in air is 340 m/s, determine the length of the pipe. [3]

c) Explain why increasing the diameter of the pipe does not significantly affect the frequency of the standing wave produced. [2]