Answered

A 4.0 g string, 0.36 m long, is under tension. The string produces a 500 Hz tone when it vibrates in the third harmonic. The speed of sound in air is 344 m/s. In this situation, the wavelength of the standing wave in the string, in SI units, is closest to:

Answer :

Answer:

[tex]\lambda = 0.24 m[/tex]

Explanation:

The string vibrates in the third harmonics, n = 3

Length of the string, l = 0.36 m

Frequency of the tone produced, f = 500 Hz

The speed of sound in air is 344 m/s

Calculate the speed of sound produced by the string in the third harmonics:

The frequency of sound is given by the formula:

[tex]f = \frac{nv}{2l} \\500 = \frac{3v}{2*0.36}\\500 * 2 * 0.36 = 3v\\v = 360/3\\v = 120 m/s\\v = \lambda f\\\lambda = v/f\\\lambda = 120/500\\\lambda = 0.24 m[/tex]

Cricetus

The wavelength of the standing wave will be "0.24 m".

Given:

  • String vibrates, [tex]n = 3[/tex]
  • Strings' length, [tex]l = 0.36 \ m[/tex]
  • Frequency, [tex]f = 500 \ Hz[/tex]
  • Speed of sound, [tex]v = 344 \ m/s[/tex]

As we know,

→ [tex]f = \frac{nv}{2l}[/tex]

then,

→ [tex]500 = \frac{3v}{2\times 0.36}[/tex]

→ [tex]360 = 3v[/tex]

      [tex]v = \frac{360}{3}[/tex]

         [tex]= 120 \ m/s[/tex]

hence,

The wavelength will be:

→ [tex]v = \lambda f[/tex]

or,

→ [tex]\lambda = \frac{v}{f}[/tex]

By substituting the values,

     [tex]= \frac{120}{500}[/tex]

     [tex]= 0.24 \ m[/tex]

Thus the approach is correct.  

Learn more about tension here;

https://brainly.com/question/13244785

Other Questions