Answer:
f = 3.1 kHz
Explanation:
given,
length of human canal =2.8 cm = 0.028 m
speed of sound = 343 m/s
fundamental frequency = ?
The fundamental frequency of a tube with one open end and one closed end is,
![f = \dfrac{v}{4L}](https://tex.z-dn.net/?f=f%20%3D%20%5Cdfrac%7Bv%7D%7B4L%7D)
![f = \dfrac{343}{4\times 0.028}](https://tex.z-dn.net/?f=f%20%3D%20%5Cdfrac%7B343%7D%7B4%5Ctimes%200.028%7D)
![f = \dfrac{343}{0.112}](https://tex.z-dn.net/?f=f%20%3D%20%5Cdfrac%7B343%7D%7B0.112%7D)
f = 3062.5 Hz
f = 3.1 kHz
hence, the fundamental frequency is equal to f = 3.1 kHz
Explanation:
Below is an attachment containing the solution.
Answer:
![\frac{r_1}{r_2}=6.9](https://tex.z-dn.net/?f=%5Cfrac%7Br_1%7D%7Br_2%7D%3D6.9)
Explanation:
According to Pascal's Law, the pressure transmitted from input pedal to the output plunger must be same:
![P_1 = P_2\\\\\frac{F_1}{A_1}=\frac{F_2}{A_2}\\\\\frac{F_1}{F_2}=\frac{A_1}{A_2}\\\\\frac{F_1}{F_2}=\frac{\pi r_1^2}{\pi r_2^2}\\\\\frac{F_1}{F_2}=\frac{r_1^2}{r_2^2}](https://tex.z-dn.net/?f=P_1%20%3D%20P_2%5C%5C%5C%5C%5Cfrac%7BF_1%7D%7BA_1%7D%3D%5Cfrac%7BF_2%7D%7BA_2%7D%5C%5C%5C%5C%5Cfrac%7BF_1%7D%7BF_2%7D%3D%5Cfrac%7BA_1%7D%7BA_2%7D%5C%5C%5C%5C%5Cfrac%7BF_1%7D%7BF_2%7D%3D%5Cfrac%7B%5Cpi%20r_1%5E2%7D%7B%5Cpi%20r_2%5E2%7D%5C%5C%5C%5C%5Cfrac%7BF_1%7D%7BF_2%7D%3D%5Cfrac%7Br_1%5E2%7D%7Br_2%5E2%7D)
where,
F₁ = Load lifted by output plunger = 2100 N
F₂ = Force applied on input piston = 44 N
r₁ = radius of output plunger
r₂ = radius of input piston
Therefore,
![\frac{r_1^2}{r_2^2}=\frac{2100\ N}{44\ N}\\\\\frac{r_1}{r_2}=\sqrt{\frac{2100\ N}{44\ N}} \\\\\frac{r_1}{r_2}=6.9](https://tex.z-dn.net/?f=%5Cfrac%7Br_1%5E2%7D%7Br_2%5E2%7D%3D%5Cfrac%7B2100%5C%20N%7D%7B44%5C%20N%7D%5C%5C%5C%5C%5Cfrac%7Br_1%7D%7Br_2%7D%3D%5Csqrt%7B%5Cfrac%7B2100%5C%20N%7D%7B44%5C%20N%7D%7D%20%5C%5C%5C%5C%5Cfrac%7Br_1%7D%7Br_2%7D%3D6.9)