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, [itex] \lambda=\frac v \nu [/itex]. 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

 

[HalfLostAndSearching]

No, the wavelengths of a standing wave and a sound wave are not necessarily the same. A standing wave is a pattern of oscillation that occurs when two waves of the same frequency and amplitude, traveling in opposite directions, interfere with each other. The wavelength of a standing wave is determined by the length of the string and the number of nodes and antinodes present. On the other hand, a sound wave is a longitudinal wave that travels through a medium, such as air, and its wavelength is determined by the frequency and speed of the wave. Therefore, the wavelength of a standing wave and a sound wave can be different depending on the properties of the medium and the source of the waves.