A 90-gram wire that is 1.0 m long is under tension.When a transverse wave of frequency 890 Hz travels down the wire,its wavelength is 0.10 m and its amplitude is 6.5 mm.What is the tension in the wire?
A)710 N
B)820 N
C)930 N
D)1,000 N
E)1,100 N

Question

Quizplus · Accepted Answer

The tension in the wire can be calculated using the formula for the velocity of a wave on a string, $v = \sqrt{\frac{T}{\mu}}$, where $v$ is the velocity of the wave, $T$ is the tension in the string, and $\mu$ is the mass per unit length of the string. The velocity can also be found using the wave equation $v = f\lambda$, where $f$ is the frequency and $\lambda$ is the wavelength. Given $f = 890$ Hz and $\lambda = 0.10$ m, we find $v = 890 \times 0.10 = 89$ m/s. The mass per unit length, $\mu$, is the total mass divided by the length, so $\mu = \frac{90}{1000} = 0.09$ kg/m. Substituting these values into the first equation and solving for $T$ gives $T = \mu v^2 = 0.09 \times 89^2 = 710.01$ N, which rounds to 710 N.

A 90-Gram Wire That Is 1