# The speed of waves on a guitar string is 122 m/s. a. What is the fundamental frequency of the...

## Question:

The speed of waves on a guitar string is 122 m/s.

a. What is the fundamental frequency of the string when the effective string length is 84.2 cm? Answer in units of Hz.

b. What is the fundamental frequency of the string when the effective string length is 57.1 cm? Answer in units of Hz.

c. What is the fundamental frequency of the string when the effective string length is 38.6 cm? Answer in units of Hz.

## Standing Wave on a String:

Assume a light string of length {eq}L {/eq} is fixed tightly at two ends. When a standing wave travels through the string with a speed of {eq}v {/eq}, then the fundamental frequency of the string can be expressed as,

{eq}f = \frac{v}{\lambda}. {/eq}

Here, the wavelength {eq}\lambda {/eq} is equal to twice the length {eq}L {/eq} of the string.

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Given data:

• Speed of the wave, {eq}v = 122 \ m/s {/eq}

The wavelength of the wave on the string can be given as,

{eq}\lambda = 2 L {/eq}

The...