Answer:
a) 3.33 ns
b) Water distance = 0.75 m
Glass distance = 0.66 m
Diamond distance = 0.41 m
Explanation:
We take the speed of light, c = m/s.
Speed = distance/time
Time = distance/speed
a)
![t=\dfrac{1}{3.0\times10^{8}}=3.33\times10^{-9}](https://tex.z-dn.net/?f=t%3D%5Cdfrac%7B1%7D%7B3.0%5Ctimes10%5E%7B8%7D%7D%3D3.33%5Ctimes10%5E%7B-9%7D)
t = 3.33 ns
b)
Refractive index, n = speed of light in vacuum / speed of light in medium
![n=\dfrac{c}{s}](https://tex.z-dn.net/?f=n%3D%5Cdfrac%7Bc%7D%7Bs%7D)
![s=\dfrac{c}{n}](https://tex.z-dn.net/?f=s%3D%5Cdfrac%7Bc%7D%7Bn%7D)
![d=s\times t](https://tex.z-dn.net/?f=d%3Ds%5Ctimes%20t)
![d=\dfrac{c}{n}\times \dfrac{1}{c}](https://tex.z-dn.net/?f=d%3D%5Cdfrac%7Bc%7D%7Bn%7D%5Ctimes%20%5Cdfrac%7B1%7D%7Bc%7D)
![d=\dfrac{1}{n}](https://tex.z-dn.net/?f=d%3D%5Cdfrac%7B1%7D%7Bn%7D)
Thus, the distance traveled in the same time is numerically equal to the reciprocal of the refractive index.
For water n = 1.333
d = 1/1.333 = 0.75 m
For glass n = 1.517
d = 0.66 m
For diamond n = 2.417
d = 0.41 m
The answer, using an indicator to measure the hydrogen ion concentration of a solution, is correct
The volume of the block of wood is given by length × width ×height
= 2.75 × 4.80 × 7.5
= 99 cm³
Density is given by mass/volume
Thus = 84.0 g/ 99 cm³
= 0.848 g/cm³
Hence; since the block is less dense than water (1 g/cm³) it will float
Answer:
81.9756 m/s
16.8 m
4.8795 Hz
Explanation:
m = Mass of string = 0.12 kg
L = Length of string = 8.4 m
T = Tension on string = 96 N
Linear density is given by
![\mu=\dfrac{m}{L}\\\Rightarrow \mu=\dfrac{0.12}{8.4}](https://tex.z-dn.net/?f=%5Cmu%3D%5Cdfrac%7Bm%7D%7BL%7D%5C%5C%5CRightarrow%20%5Cmu%3D%5Cdfrac%7B0.12%7D%7B8.4%7D)
Spee of the wave is given by
![v=\sqrt{\dfrac{T}{\mu}}\\\Rightarrow v=\sqrt{\dfrac{96}{\dfrac{0.12}{8.4}}}\\\Rightarrow v=81.9756\ m/s](https://tex.z-dn.net/?f=v%3D%5Csqrt%7B%5Cdfrac%7BT%7D%7B%5Cmu%7D%7D%5C%5C%5CRightarrow%20v%3D%5Csqrt%7B%5Cdfrac%7B96%7D%7B%5Cdfrac%7B0.12%7D%7B8.4%7D%7D%7D%5C%5C%5CRightarrow%20v%3D81.9756%5C%20m%2Fs)
The speed of the waves on the string is 81.9756 m/s
Wavelength is given by
![\lambda=2L\\\Rightarrow \lambda=2\times 8.4\\\Rightarrow \lambda=16.8\ m](https://tex.z-dn.net/?f=%5Clambda%3D2L%5C%5C%5CRightarrow%20%5Clambda%3D2%5Ctimes%208.4%5C%5C%5CRightarrow%20%5Clambda%3D16.8%5C%20m)
The longest possible wavelength is 16.8 m
Frequency is given by
![f=\dfrac{v}{\lambda}\\\Rightarrow f=\dfrac{81.9756}{16.8}\\\Rightarrow f=4.8795\ Hz](https://tex.z-dn.net/?f=f%3D%5Cdfrac%7Bv%7D%7B%5Clambda%7D%5C%5C%5CRightarrow%20f%3D%5Cdfrac%7B81.9756%7D%7B16.8%7D%5C%5C%5CRightarrow%20f%3D4.8795%5C%20Hz)
The frequency of the wave is 4.8795 Hz