Are the wavelength of standing wave and sound wave produced same?

[somecelxis]

Homework Statement

a string is tightened at 2 ends. the string is then plucked , a standing wave is produced. are the wavelength of standing wave and sound wave produced same?

Homework Equations

The Attempt at a Solution

 

[ShayanJ]

No.
We have, for any wave, $\lambda=\frac v \nu$. The frequency of the standing wave and the sound wave are the same, but their propagation velocities, on the string and in the air respectively, are different and so their wavelengths are different.

 

[somecelxis]

how do you know that The frequency of the standing wave and the sound wave are the same, but their propagation velocities, on the string and in the air respectively, are different why?

 

[ehild]

The speed of a wave along a string is determined by the tension in it (T) and the linear density (μ): v=√(T/μ). The speed of sound is about 300 m/s in air at room temperature.

ehild