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Water Wave

Theme C - Wave Behaviour 

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Rocket

Theme A - Space, Time & Motion

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Thermometer

Theme B - The Particulate Nature Of Matter

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Magnifying Glass Tilted Right

Theme D - Fields

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Microscope

Theme E - Nuclear & Quantum Physics

Hello there! Ready to jam out on the physics of strings? Let&#39;s tune in!

<ul>
	<li>Fundamental Concept
	<ul>
		<li>The pitch of a note on a stringed instrument is influenced by
		<ul>
			<li>The length of the string 📏</li>
			<li>The tension in the string 🌀</li>
		</ul>
		</li>
	</ul>
	</li>
	<li>Tuning Instruments
	<ul>
		<li>The main way to get the right note or &quot;tune&quot; an instrument is by adjusting the tension.</li>
		<li>Musicians play individual notes by adjusting the lengths of the strings.</li>
	</ul>
	</li>
</ul>

Real-World Example 🌍

Think of a guitar. When you twist the tuning pegs, you&#39;re adjusting the tension in the strings to get the right sound. When you press down on a fret, you&#39;re changing the length of the string that&#39;s vibrating!

<ul>
	<li>Relation between String Length (L) and Frequency (f)
	<ul>
		<li>First harmonic (Fundamental frequency): Half a wavelength fits in the length (L) of the string.
		<ul>
			<li>L = \(\frac {λ}{2}\)​</li>
			<li>Equation: f1​= \(\frac {c}{2L}\)​ (where c is the speed of the wave in the string)</li>
		</ul>
		</li>
	</ul>
	</li>
	<li>Second harmonic: A full wavelength fits in L.
	<ul>
		<li>f2​ = 2f1​</li>
	</ul>
	</li>
	<li>Third harmonic: One and a half wavelengths fit in L.
	<ul>
		<li>f3​=3f1​</li>
	</ul>
	</li>
	<li>For nth harmonic
	<ul>
		<li>fn ​= nf1​</li>
	</ul>
	</li>
</ul>

<ul>
	<li>What&#39;s a node? It&#39;s a point where there&#39;s no motion on a vibrating string. The spots that don&#39;t seem to be moving when you pluck a string!</li>
	<li>Fun fact&nbsp;Musicians play around with harmonics to change the sound of their instruments. By touching the middle of a string, for instance, they can stop certain harmonics and produce a unique sound.</li>
</ul>

Real-World Example 🌍

Ever heard a guitar player lightly touch a string and produce a &#39;ping&#39; sound? They&#39;re playing with harmonics! By touching the string at specific points, they can make it ring in unique ways.

Given

<ul>
	<li>String of length: 0.90m</li>
	<li>Wave speed: 270 m/s</li>
	<li>P and Q are two particles on the string.</li>
</ul>

Questions

<ul>
	<li>Phase difference between P and Q

	<ul>
		<li>Since P and Q are in the same nodal region, their phase difference is zero.</li>
	</ul>
	</li>
	<li>Frequency of the second harmonic
	<ul>
		<li>&lambda; (wavelength) = Length of string = 0.90m</li>
		<li>Using the equation \(f = \frac {c}{λ}\)\(f = \frac {270m /s}{0.90m} = 300Hz\)</li>
	</ul>
	</li>
	<li>If the string is clamped at Q
	<ul>
		<li>Q&#39;s position: one-third the length of the string from the left end.</li>
		<li>Q becomes a node and the lowest frequency mode will be the third harmonic.</li>
		<li>New wavelength: \(2×\frac {1}{3} × 0.90m = 0.60m\)&times;0.90m=0.60m</li>
		<li>Using the equation f = \(\frac {270m / s}{0.60m}\)​=450Hz</li>
	</ul>
	</li>
</ul>

Real-World Example 🌍

Imagine a jump rope tied at both ends, representing our string. When you shake it once (first harmonic), you see a single bump. Shake it faster (second harmonic), and you see two bumps. The faster or harder you shake, the more bumps or waves you&#39;ll see!

&nbsp;

Remember, every string instrument from the electric guitar to the ancient sitar uses these principles. So next time you jam out, give a nod to the science making it all possible! 🎸🎶🔬

Understanding String Harmonics: The Physics Behind Music

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Higher Level

Physics HL

Theme C - Wave Behaviour

Understanding String Harmonics: The Physics Behind Music

Table of content

Understanding pitch & string instruments 🎻

Unlock the Full Content!

Theme C - Wave Behaviour

Understanding String Harmonics: The Physics Behind Music

Table of content

Understanding pitch & string instruments 🎻

Unlock the Full Content!