Respuesta :
Given data:
* The fundamental length of pipe is,
[tex]L_1=0.25\text{ m}[/tex]* The next resonant length of pipe is,
[tex]L_2=0.75\text{ m}[/tex]* The speed of the sound is v = 338 m/s.
Solution:
The fundamental length of the pipe in terms of the wavelength is,
[tex]L_1=\frac{1}{4}\lambda[/tex]The second resonant length of the pipe in terms of wavelength is,
[tex]L_2=\frac{3}{4}\lambda[/tex]Substracting both the values,
[tex]\begin{gathered} L_2-L_1=\frac{3}{4}\lambda-\frac{1}{4}\lambda \\ L_2-L_1=\frac{2}{4}\lambda \\ L_2-L_1=\frac{1}{2}\lambda \end{gathered}[/tex]Substituting the known values,
[tex]\begin{gathered} 0.75-0.25=\frac{1}{2}\times\lambda \\ 0.5=\frac{1}{2}\times\lambda \\ \lambda=1\text{ m} \end{gathered}[/tex]Thus, the value of the wavelength of sound emitted by the tuning fork is 1 meter.
(b). The frequency of the sound is,
[tex]\begin{gathered} v=f\lambda \\ f=\frac{v}{\lambda} \\ f=\frac{338}{1} \\ f=338\text{ Hz} \end{gathered}[/tex]Thus, the frequency of sound is 338 Hz.
