Question

A string of length 10.0 m is tied between two posts and plucked. This sends a wave down the string moving at a speed of 130 m/s with a frequency of 215 Hz. How many complete wavelengths of this wave will fit on the string?

Answer 1

16.

Step-by-step explanation:

• In any wave, by definition, there exists a fixed relationship between the speed v, the frequency f , and the wavelength λ, as follows:

`v = \lambda * f (1)`

• In our case, v = 130 m/s and f= 215 Hz, so solving for λ in (1), we get:

`\lambda = (v)/(f) = (130m/s)/(215 hz) = 0.61 m (2)`

• In order to know how many wavelengths of this wave will fit on the string, we need just do divide the length of the string (10.0 m) over one single wavelength, as follows:

`n = (L)/(\lambda) = (10.0m)/(0.61m) = 16.4 (3)`

• Since we need to take the integer value from this expression, the number of complete wavelengths that will fit on this string is just 16.