Question

Consider a string with a length of (47.5 A) cm tied at both end (like on a stringed instrument). If the frequency of the first harmonic on the string is (245 B) Hz, determine the speed of the wave in the string. Post your answer in m/s and with 3 significant figures.

Answer 1

To solve this problem it is necessary to apply the concepts related to wavelength as a function of frequency and speed, as well as to determine the wavelength as a function of length.

From the harmonic vibration generated we know that the total length of the string will be equivalent to a half of the wavelength, that is

$L = \frac{\lambda}{2} \rightarrow \lambda = 2L$

Where,

$\lambda =$ Wavelength

Therefore the wavelength for us would be,

$\lambda = 2*47.5cm = 95cm = 0.95m$

From the relationship of speed, frequency and wavelength we know that

$\lambda = \frac{v}{f} \rightarrow v = \lambda f$

$v = (0.95m)(245Hz)$

$v = 232.75 m/s$

Therefore the speed of the wave is 232.75m/s