Standing waves are caused by two waves interfering with each other, usually a wave and its reflection. A standing wave on a string is formed when the string length is a multiple of half wavelengths. The fundamental frequency is the lowest frequency at which a standing wave can form, which is equal to the wave speed divided by twice the string length. Harmonics are integer multiples of the fundamental frequency. Nodes are points that always have zero amplitude, while antinodes are points that have maximum amplitude.

1. Standing Waves A guide to what they are and where they are used

2. To summarise so far: Waves superpose when they meet They can interfere constructively when ‘In-Phase’ and destructively when ‘anti-phase’ Waves interfere in a stable manner when they are coherent – they have a constant phase difference Waves can be represented by a phasor that rotates anticlockwise The angular movement can be represented in Radians, where 2π Radians is the equivalent to 360 o and 1 wavelength (λ)

3. This lesson we will See how a standing wave in a string is set up Understand how a standing wave is formed in terms of wavelengths Find out what a fundamental frequency of a standing wave is Understand the term resonance, harmonic, node and antinode

4. Standing Waves These are caused by 2 waves interfering They are usually caused by a wave and its reflection

5. Let’s see one in action...

6. Standing Wave Properties A string has a wavelength that is double the length of string 1/2 Wavelength

7. Standing Wave Properties What is the next wavelength? Try to draw it... 1/2  Length = n  /2 I.e. it is a multiple of half wavelengths Length

8. Wavelengths For all values of n, wavelengths are multiples of 1/2  What is the equation for speed? What are the wavelengths opposite if L = 30cm?

9. Fundamental Frequency This is the lowest frequency that a system can resonate at - it is the lowest frequency that a standing wave can form at on a string Using; Speed = Frequency x Wavelength Therefore Fundamental Frequency = speed / 2L What is the fundamental frequency the previous string (30cm) assuming the speed is 60ms -1 ?

10. Fundamental Frequency What is the fundamental frequency for the previous string (30cm) assuming the speed is 60ms -1 ? 1/2  30cm Fundamental Frequency = 60 / 2 x 0.3 = 100Hz

11. Standing Wave Properties Harmonics These are the multiples of the fundamental frequency For string this is a whole number Frequency = v/  L harmonics = n x frequency

12. Harmonics An harmonic is a multiple of the fundamental frequency For our piece of string, what are the harmonics? 1/2  30cm Harmonics = n x Fundamental Frequency = 200, 300, 400…. N x 100Hz

13. Nodes and Antinodes These are areas of the wave that; Node - always add up to zero Antinode - waves combine to make a large oscillation

14. Some Questions 1.A source of sound waves of frequency 570Hz emits a note of wavelength 0.6m in air at 20 o C. What is the speed of sound at this temperature? 2.A stationary wave is formed in a string with antinodes every 150mm. What is the wavelength of the standing wave? 3.A loudspeaker points directly at a wall 3m away and emits a note of frequency 680Hz. A standing wave is formed. If the speed is 340m/s what will be the separation between minimum intensities (nodes)?

15. Some Questions 1.A source of sound waves of frequency 570Hz emits a note of wavelength 0.6m in air at 20 o C. What is the speed of sound at this temperature? 342m/s 2.A stationary wave is formed in a string with antinodes every 150mm. What is the wavelength of the standing wave? 300mm 3.A loudspeaker points directly at a wall 3m away and emits a note of frequency 680Hz. A standing wave is formed. If the speed is 340m/s what will be the separation between minimum intensities (nodes)? 0.25m