Waves - Standing Waves

Describe how a standing wave is formed

A standing wave is formed from the combination of 2 identical waves moving through each other in opposite directions

Do standing waves transfer energy? Why?

No. Although each of the two waves in a standing wave carry energy, they are in opposite directions. Energy is therefore 'trapped' in the standing wave and changes between KE and PE as particles vibrate forwards and backwards.

Describe the difference between nodes and antinodes

Nodes are fixed at ends. Antinodes are the max displacement, or open ends.

How do you calculate the distance between 2 adjacent antinodes?

d = λ/2

How can you produce a standing wave?

Send a wave towards a barrier so that the reflected wave travels back through the incident wave

Explain resonance

The tendency of an object to have a greater amplitude when the frequency of its oscillations (driving freq) is = to its natural freq of the system (resonant freq)

Name the three standing wave applications

String, closed pipe and open pipe

The first harmonic is also known as the...

Fundamental frequency

Eqn for the λ of a string...

λ = 2L/n

Eqn for the λ of a closed pipe (open at one end, closed at the other end)...

λ = 4L/n

Eqn for an open pipe (open/closed at BOTH ends)...

λ = 2L/n

How do you work out the harmonic number of a closed pipe (open at one end, closed at the other end)?

Harmonic = (2 x overtones) + 1

Closed pipes can only have _______ harmonics

odd

To play a note with a different pitch, what must you change? (fundamental freq)

The freq of the fundamental
- by changing λ
- which will then change L
- gives you a shorter string, shorter λ, so f will increase

To play a note with a different pitch, what must you change? (tension force)

Increase the tension force (tuning pegs of an instrument change the tension applied to strings)
- the speed of wave in the string increases
- then freq increases and hence the pitch increases

A clarinet (closed pipe at one end) produces the fundamental frequency and several harmonics, why does it not produce any even harmonics? (first image at the top is the first harmonic of a close pipe)

Top picture.
The clarinet is closed at one end, so this closed end has a node while the open ends have an antinode. The tube can only sustain odd harmonics because the tube 'fits' only an odd number of quarter wavelengths. Even harmonics require nodes or antinodes at both ends because length is an even number of quarter wavelengths.

Describe 4 differences between standing waves and travelling waves

- SW do not transfer energy, TW do
- SW have nodes and antinodes, TW do not
- SW have 2 sources, TW only require 1 source
- SW require interference, TW do not

Look at the image. Mike is 6m from one end and Kate is 6m from the other end. Explain how it is possible for Mike and Kate to cause the bridge to oscillate in the 2nd harmonic.
- explain how they set up a standing wave
- explain why they choose to stand in the positions stated
- explain the phase relationship between their collisions

Image is of a second harmonic.
- By jumping up and down they send transverse waves which will travel along the bridge, hit a closed end and then reflect back. The 2 waves will interfere and create a standing wave.
- they must stand at the 1/4 and 3/4 positions because this is where the antinodes are located for the 2nd harmonic. Mike and Kate are the antinodes essentially.
- they must jump 180 degrees out of phase, as adjacent antinodes are out of phase. they must also jump at the correct frequency (half of the period for Mike and Kate. (T= 1.8/2 = 0.9s)

One pipe has a fund freq of 350 Hz while another has a fund freq of 395 Hz. Which pipe is longer

The 350 Hz pipe is longer. it produces a longer frequency so it has a longer wavelength and therefore a longer pipe length. The wave length of a standing wave is proportional to the length. so L=v/f ... v stays constant, so a lower f means a larger L, longer wavelength and longer length of pipe.

Two pipes are blown, producing similar freq heard. State the name of this phenomena and explain how it you can hear a variation in loudness...

This is called beating (beats)
- the two pipes produce similar but different freq
- at one time the 2 waves arrive in phase and add con. (loud)
- a short time later the 2 waves arrive out of phase and add des. (quiet)

What is wavelength proportional to?

length of the first harmonic/fundamental frequency
so... λ = l = v/f
* length of the first harmonic. if you then needed to find the length of the 3rd harmonic, make your expression for L, then find l, then state that λ is prop to l, so sub l into L eqn for length of pipe in 3rd harmonic. (2016 1d)

The air flowing through a pipe produces oscillations with a range of frequencies. Explain why not all frequencies produce standing waves in the pipe. (a close pipe - 2014 Q1 b)

the wavelength of the standing sound wave forming in the pipe must allow a position of permanent con int (antinode) to occur at the open end. There will be a position of permanent des int (node) at the closed end of the pipe because the waves reflect back out of phase.
The 'sharp lip' of the pipe generates sound waves that have a larger range of different freq, and some of these will produce a wavelength that can meet the condition above.

explain why the differences in length of organ pipes affect the sounds that are heard.

the frequency of the sound produced acts inversely to the wavelength (v=fλ). λ is proportional to the length of the pipe (L). so we can write the eqn as v=fL. If you had a longer pipe, you produce a longer λ of sound (L is prop to λ). If L/λ increase, then f is going to decrease (produce a lower frequency) to due to the inverse relationship between f and λ/L. A lower freq is a lower pitch, and this is how different sounds are heard.

Explain how a standing wave is produced in a pipe that is closed at one end?