A 2.00 m long string transmits waves at 12.9 m/s. At what
frequency will it create standing
waves with 3 loops?
(Unit = Hz)

The frequency at which the string will create a standing wave be  with three loops is 8.6 Hz

Explanation:

The speed of the of the wave, v = 12.9 m/s

The number of loops of the standing wave = 3 loops

The length of the string = 2.00 m

Given that one loo = half of the wavelength, we have;

Three loops = 3 × half = One and half wavelength  = 1.5·λ

The frequency of a wave = f = v/λ

Therefore, we have;

The frequency, f = 12.9/1.5 = 8.6 Hz

The frequency at which the string will create a standing wave be  with three loops = 8.6 Hz.

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