| A wave in a string has an amplitude of 2 cm. |
| The wave travels in the +ve direction of x axis with a speed of \[128\,m{{s}^{-1}}\] and it is noted that 5 complete waves fit in 4 m length of the string. |
| The equation describing the wave is [AIPMT (S) 2009] |
A) \[y=(0.02)\,m\,\sin \,(7.85x+1005\,t)\]
B) \[y=(0.02)\,m\,\sin \,(15.7x-2010\,t)\]
C) \[y=(0.02)\,m\,\sin \,(15.7x+2010\,t)\]
D) \[y=(0.02)\,m\,\sin \,(7.85x-1005\,t)\]
Correct Answer: D
Solution :
| Key Idea Find the parameters and put in the general wave equation. |
| Here, \[A=2cm\] direction \[=+ve\,x\] direction |
| \[v=128\,m{{s}^{-1}}\] and \[\lambda =4\] |
| Now, \[k=\frac{2\pi }{\lambda }=\frac{2\pi \times 5}{4}=7.85\,\] |
| and \[v=\frac{\omega }{k}=128\,m{{s}^{-1}}\] |
| \[\Rightarrow \] \[\omega =v\times k=128\times 7.85\] |
| \[=\text{ }1005\] |
| As, \[y=A\,\sin \,(kx-\omega t)\] |
| \[\therefore \] \[y=2\sin \,(7.85\times -1005\,t)\] |
| \[=(0.02)\,m\,\sin (7.85x\times 1005t)\] |
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