Question

A transverse wave of frequency 4 Hz travels at a speed of 6 m/2 along a rope. What would be the speed of a 12 Hz wave long this same rope?

Answer 1

Given data

*The given frequency of the transverse wave is f = 4 Hz

*The given speed of the wave is v = 6 m/s

*The other given frequency is 12 Hz

The formula for the wavelength is given as

`\lambda=(v)/(f)`

Substitute the known values in the above expression as

`\begin{gathered} \lambda=(6)/(4) \\ =1.5\text{ m} \end{gathered}`

Now, the speed of the wave is calculated as

`v_1=f_1\lambda`

Substitute the known values in the above expression as

`\begin{gathered} v_1=(12)(1.5) \\ =18\text{ m/s} \end{gathered}`

Hence, the speed of a 12 Hz wave along this same rope is 18 m/s