The tension in a string with a linear density of 0.0010 kg/m is 0.40 N.A 100 Hz sinusoidal wave on this string has a wavelength of:
A)0.20 cm
B)2.0 cm
C)5.0 cm
D)20 cm
E)400 cm

Question

Quizplus · Accepted Answer

The velocity of a wave on a string is given by $v = \sqrt{\frac{T}{\mu}}$, where $T$ is the tension in the string and $\mu$ is the linear density. Here, $T = 0.40 \, \text{N}$ and $\mu = 0.0010 \, \text{kg/m}$, so $v = \sqrt{\frac{0.40}{0.0010}} = \sqrt{400} = 20 \, \text{m/s}$.The wavelength $\lambda$ can be found using the relationship $v = f\lambda$, where $f$ is the frequency. Given $f = 100 \, \text{Hz}$, we have $20 = 100\lambda$, which gives $\lambda = \frac{20}{100} = 0.20 \, \text{m}$ or $20 \, \text{cm}$.

The Tension in a String with a Linear Density of 0.0010