Answer:
Explanation:
Two frequencies with magnitude 150 Hz and 750 Hz are given
For Pipe open at both sides
fundamental frequency is 150 Hz as it is smaller
frequency of pipe is given by
![f=\frac{nv}{2L}](https://tex.z-dn.net/?f=f%3D%5Cfrac%7Bnv%7D%7B2L%7D)
where L=length of Pipe
v=velocity of sound
for n=1
and f=750 is for n=5
thus there are three resonance frequencies for n=2,3 and 4
For Pipe closed at one end
frequency is given by
![f=\frac{(2n+1)}{4L}\cdot v](https://tex.z-dn.net/?f=f%3D%5Cfrac%7B%282n%2B1%29%7D%7B4L%7D%5Ccdot%20v)
for n=0
![f_1=\frac{v}{4L}](https://tex.z-dn.net/?f=f_1%3D%5Cfrac%7Bv%7D%7B4L%7D)
![f_1=150\ Hz](https://tex.z-dn.net/?f=f_1%3D150%5C%20Hz)
for n=2
![f_2=\frac{5v}{4L}](https://tex.z-dn.net/?f=f_2%3D%5Cfrac%7B5v%7D%7B4L%7D)
Thus there is one additional resonance corresponding to n=1 , between
and ![f_2](https://tex.z-dn.net/?f=f_2)
Answer:
A
Explanation:
Frequency is defined by repetitions or periods per second. If we take any segment from each graph, we would see that graph A has the most repetitions per second.
The period of A is the shortest since the frequency is equal to 1/T, the smaller the period, the higher the frequency.
The work done is ![2.8125 \times 10^{5} \mathrm{J}](https://tex.z-dn.net/?f=2.8125%20%5Ctimes%2010%5E%7B5%7D%20%5Cmathrm%7BJ%7D)
Work Done = Change in Kinetic Energy (ΔKE)
<u>Explanation</u>
In first 1 hour it travels 72 km
So, Velocity = ![\frac{\text { distance }}{\text { time }}=\frac{72}{1} k m / h=72 \mathrm{km} / \mathrm{h}=\frac{72000}{3600} \mathrm{m} / \mathrm{s}=20 \mathrm{m} / \mathrm{s}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%20%7B%20distance%20%7D%7D%7B%5Ctext%20%7B%20time%20%7D%7D%3D%5Cfrac%7B72%7D%7B1%7D%20k%20m%20%2F%20h%3D72%20%5Cmathrm%7Bkm%7D%20%2F%20%5Cmathrm%7Bh%7D%3D%5Cfrac%7B72000%7D%7B3600%7D%20%5Cmathrm%7Bm%7D%20%2F%20%5Cmathrm%7Bs%7D%3D20%20%5Cmathrm%7Bm%7D%20%2F%20%5Cmathrm%7Bs%7D)
or, Initial Velocity (u) = 20 m/s
Similarly for the next hour it covers 90 km
So, Velocity = ![\frac{\text { distance }}{\text { time }}=\frac{90}{1} k m / h=90 \mathrm{km} / \mathrm{h}=\frac{90000}{3600} \mathrm{m} / \mathrm{s}=25 \mathrm{m} / \mathrm{s}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%20%7B%20distance%20%7D%7D%7B%5Ctext%20%7B%20time%20%7D%7D%3D%5Cfrac%7B90%7D%7B1%7D%20k%20m%20%2F%20h%3D90%20%5Cmathrm%7Bkm%7D%20%2F%20%5Cmathrm%7Bh%7D%3D%5Cfrac%7B90000%7D%7B3600%7D%20%5Cmathrm%7Bm%7D%20%2F%20%5Cmathrm%7Bs%7D%3D25%20%5Cmathrm%7Bm%7D%20%2F%20%5Cmathrm%7Bs%7D)
or, Final Velocity (v) = 20 m/s
Work done = Change in Kinetic Energy (ΔKE)
Work done = ΔKE = ![\frac{1}{2} m v^{2}-\frac{1}{2} m u^{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20m%20v%5E%7B2%7D-%5Cfrac%7B1%7D%7B2%7D%20m%20u%5E%7B2%7D)
ΔKE = ![\frac{1}{2} m\left(v^{2}-u^{2}\right)=\frac{1}{2} \times\left(2.5 \times 10^{3}\right) \times\left(25^{2}-20^{2}\right)](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20m%5Cleft%28v%5E%7B2%7D-u%5E%7B2%7D%5Cright%29%3D%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%5Cleft%282.5%20%5Ctimes%2010%5E%7B3%7D%5Cright%29%20%5Ctimes%5Cleft%2825%5E%7B2%7D-20%5E%7B2%7D%5Cright%29)
=
= 281250 joule
= ![2.8125 \times 10^{5} \mathrm{J}](https://tex.z-dn.net/?f=2.8125%20%5Ctimes%2010%5E%7B5%7D%20%5Cmathrm%7BJ%7D)
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