A wire that is 1.0 m long with a mass of 90 g is under a tension of 710 N.When a transverse wave travels on the wire,its wavelength is 0.10 m and its amplitude is 6.5 mm.What is the frequency of this wave?
A)890 Hz
B)920 Hz
C)1000 Hz
D)1200 Hz
E)1500 Hz

Question

Quizplus · Accepted Answer

The wave speed is given by v = sqrt(T/m), where T is the tension and m is the mass per unit length. The mass per unit length is m = M/L, where M is the total mass and L is the length. So, v = sqrt(T/(M/L)) = sqrt(TL/M). The frequency is given by f = v/lambda, where lambda is the wavelength. So, f = sqrt(TL/M)/lambda. Plugging in the given values, we get f = sqrt(710 N * 1.0 m / 0.090 kg) / 0.10 m = 890 Hz.

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