Oscillation of a $600 H z$ tuning fork sets up standing waves in a string clamped at both ends. The wave speed for the string is $400 m / s .$ The standing wave has four loops and an amplitude of $2.0 m m$ . What is the length of the string?

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Solution

since the string has four loops its length must be two wavelengths.
That is, $λ = L / 2$ , where $λ$ is the wavelength and $L$ is the length of the string.
The wavelength is related to the frequency $f$ and wave speed $v$ by $λ = v f$ , so $L / 2 = v / f$ and
$L = 2 v / f = 2 (400 m / s) / (600 H z) = 1.3 m$

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Oscillation of a 600Hz tuning fork sets up standing waves in a string clamped at both ends. The wave speed for the string is 400m/s. The standing wave has four loops and an amplitude of 2.0mm. What is the length of the string?

since the string has four loops its length must be two wavelengths. That is, λ=L/2, where λ is the wavelength and L is the length of the string. The wavelength is related to the frequency f and wave speed v by λ=vf, so L/2=v/f andL=2v/f=2(400m/s)/(600Hz)=1.3m

Oscillation of a $600 H z$ tuning fork sets up standing waves in a string clamped at both ends. The wave speed for the string is $400 m / s .$ The standing wave has four loops and an amplitude of $2.0 m m$ . What is the length of the string?