A tuning fork with a frequency of 440 Hz is connected to a long...

Given parameters are:

Frequency, $f = 440 \text{ Hz}$

Linear mass density, $\mu = 0.01 \text{ kg m}^{-1}$

Tension, $T = 49 \text{ N}$

The wave speed $v$ on a stretched string is given by:

$v = \sqrt{\dfrac{T}{\mu}}$

Substituting the given values:

$v = \sqrt{\dfrac{49}{0.01}} = \sqrt{4900} = 70 \text{ m s}^{-1}$

The wavelength $\lambda$ is related to the wave speed and frequency by:

$\lambda = \dfrac{v}{f}$

Substituting the values:

$\lambda = \dfrac{70}{440} \text{ m} = \dfrac{7}{44} \text{ m}$

Converting to centimeters:

$\lambda = \dfrac{700}{44} \text{ cm} \approx 15.9 \text{ cm} \approx 16 \text{ cm}$

The wave speed is $70 \text{ m s}^{-1}$ and the wavelength is $16 \text{ cm}$.