g a 62 cm guitar string produces a sound wave with a fundamental frequency of 160 hz the speed of sound in air is 339 m/s determine the ratio of the wavelength of the waves that travel on the string to the wavelength of the generated sound wave

The ratio of the wavelength of the waves that travel on the string to the wavelength of the generated sound wave is 0.585

Explanation:

Given;

length of the guitar string, L = 62 cm = 0.62 m

fundamental frequency of the sound, f = 160 Hz

speed of sound in air, v = 339 m/s

The wavelength of the sound that travels on the string is calculated as follows;

for fundamental frequency; Length of the string = Node ------->  Node

Length of string, L = λ/2

λ₁ = 2 x L

λ₁ = 2 x 0.62 m

λ₁ = 1.24 m

The wavelength of the generated sound wave that travels in the air is calculated as follows;

λ₂ = v / f

λ₂ =  339 / 160

λ₂ = 2.12 m

The ratio of the two wavelengths is calculated as;