Answer:
(a) 3400 Hz
(b) 3.33 cm
(c) It increases
Explanation:
(a) The ear, being open at one end and closed at the other, is equivalent to a closed pipe. For a closed pipe, the first resonant frequency occurs when one quarter of the wavelength is equal to the length of the pipe.
[tex]\dfrac{\lambda}{4}=l[/tex]
[tex]\lambda = 4l[/tex]
Speed is given by
[tex]v=f\lambda[/tex] where f is the frequency.
[tex]f=\dfrac{v}{\lambda}[/tex]
At the first resonant frequency,
[tex]f=\dfrac{v}{4l}[/tex]
[tex]f=\dfrac{340}{4\times2.5\times10^{-2}} = 3400\text{ Hz}[/tex]
(b) At second resonance,
[tex]\dfrac{3}{4}\lambda=l[/tex]
[tex]\lambda=\dfrac{4}{3}l[/tex]
[tex]\lambda=\dfrac{4}{3}\times2.5\times10^{-2} \text{ m} = 3.33\times10^{-2} \text{ m} = 3.33\text{ cm}[/tex]
(c) It increases. Sound travels faster in a liquid than in gas. From the formula in (a), the resonant frequency increases with speed.
