- Investigate and model the behavior of standing waves on strings and/or in pipes to relate quantitatively the fundamental and harmonic frequencies of the waves that are produced to the physical characteristics (e.g length, mass, tension, wave velocity) of the medium
To make today’s lesson easier, we will think of a guitar.
Have you ever played a guitar and wondered how picking a string creates a sound? Essentially, picking a guitar string creates a standing wave which causes it to vibrate at a certain frequency, this is then amplified to produce the sound.
A standing wave also known as a stationary wave is a wave which does not appear to move. This occurs due to the superposition of two waves moving in opposite directions. When you pick a guitar string, you send a wave with travels along the length of the string then reflects off the end and returns back. This means two waves are created which are travelling in opposite directions hence they have constructive and deconstructive interference.
The nodes are the regions which remain stationary in a standing wave. The anti nodes are the regions which will oscillate with maximum displacement. To change the number of nodes and anti nodes in a string, you must change the frequency you are oscillating the string.
Increasing the length of the string makes the pitch lower, as you play higher threats (therefore, shortening the length of the string) on the guitar the pitch of the guitar gets higher.
Increasing the mass of the string makes the pitch lower, as you play the heavier strings on a guitar the pitch gets lower.
Increasing the tension on the string makes the pitch higher, as you tighten the tuning pegs on a guitar the tension in the string increases making the guitar more high pitched.
Changing the mass and tension in the string will change the velocity of the waves in the string. The less mass per unit length in the string and the more tension the greater the wave velocity in the string.
In order to model this phenomena, you can tie a skipping rope to the leg of a chair and shake the en back and forth. This creates a wave which will travel through the string and reflect off the end. When it returns, it will interfere hence creating a standing wave evident by the presence of nodes. Try changing the frequency – this should increase the number of nodes.
What effect will the following have on frequency of the wave? [1 mark each]
- Using a thinner and lighter guitar string
- Playing on a higher threat, increasing the length of the string
- Picking the guitar string at a faster rate
- Lowering the tension in the guitar string
Explain what is required to create a standing wave in string and what features this would have? [4 marks]
Evaluate a model which you used to demonstrate how standing waves can be created and how they work? [6 marks]