Question

The speed of a wave travelling along a 0.650 m guitar string is 320 m/s at n = 5 the frequency is 1230 Hz. What is the frequency of a string wave speed of 240.0 m/s is used?

Answer 1

The frequency of a string wave is 922.5 Hz

Step-by-step explanation:

Given;

length of the string, L = 0.65 m

initial speed of the string wave at n = 5, v₁ = 320 m/s

initial frequency of the wave speed, f₁ = 1230 Hz

final speed of the string wave at n = 5, v₂ = 240.0 m/s

final frequency of the wave speed, f₂ = ?

speed of wave is related to frequency of wave and wavelength by the following equation;

V = Fλ

If the wavelength is constant at n = 5, then

`\lambda = (V_1)/(f_1) = (V_2)/(f_2)\\\\f_2 = (f_1V_2)/(V_1) \\\\f_2 =(1230*240)/(320) \\\\f_2 = 922.5 \ Hz`

Therefore, the frequency of a string wave, if speed of 240.0 m/s is used is 922.5 Hz