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Two identical guitar strings are prepared such that they have the same length ( 0.66 m ) and are under the same amount of tension. The first string is plucked at one location, primarily exciting the fourth harmonic. The other string is plucked in a different location, primarily exciting the second harmonic. The resulting sounds give rise to a beat frequency of 351 Hz . What is the wave propagation speed on the guitar strings

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Answer:

[tex]154.44\ \text{m/s}[/tex]

Explanation:

L = Length of guitar string = 0.66 m

Difference of fourth and first harmonic = 351 Hz

v = Wave propagation speed on the guitar strings

So,

[tex]\dfrac{4v}{2L}-\dfrac{v}{2L}=351\\\Rightarrow \dfrac{3v}{2L}=351\\\Rightarrow v=\dfrac{351\times 2\times 0.66}{3}\\\Rightarrow v=154.44\ \text{m/s}[/tex]

The wave propagation speed on the guitar strings is [tex]154.44\ \text{m/s}[/tex].

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