SATHEE: Wave Motion 2 Question 33

Wave Motion 2 Question 33

33. A wave disturbance in a medium is described by $y (x, t) = 0.02 \cos (50 π t + \frac{π}{2}) \cos (10 π x)$ , where $x$ and $y$ are in metre and $t$ is in second.

$(1995, 2 M)$

(a) A node occurs at $x = 0.15 m$

(b) An antinode occurs at $x = 0.3 m$

(d) The wavelength of wave is $0.2 m$

Show Answer

Answer:

Correct Answer: 33. (a, b, c, d)

Solution:

It is given that $y (x, t) = 0.02 \cos (50 π t + π / 2) \cos (10 π x)$

$≅ A \cos (ω t + π / 2) \cos k x$

Node occurs when $k x = \frac{π}{2}, \frac{3 π}{2}$ etc.

$10 π x = \frac{π}{2}, \frac{3 π}{2} \Rightarrow x = 0.05 m, 0.15 m$

option (a)

Antinode occurs when $k x = π, 2 π, 3 π$ etc.

$\begin{array}{ll} 10 π x = π, 2 π, 3 π etc. \\ \Rightarrow & x = 0.1 m, 0.2 m, 0.3 m option (b) \end{array}$

Speed of the wave is given by,

$v = \frac{ω}{k} = \frac{50 π}{10 π} = 5 m / s$

option (c)

Wavelength is given by,

$λ = \frac{2 π}{k} = \frac{2 π}{10 π} = (\frac{1}{5}) m = 0.2 m$

option (d)

पिछला

अगला

Wave Motion 2 Question 33

33. A wave disturbance in a medium is described by $y (x, t) = 0.02 \cos (50 π t + \frac{π}{2}) \cos (10 π x)$ , where $x$ and $y$ are in metre and $t$ is in second.

Answer:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Wave Motion 2 Question 33

33. A wave disturbance in a medium is described by y(x,t)=0.02cos⁡(50πt+π2)cos⁡(10πx), where x and y are in metre and t is in second.

Answer:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Menu

33. A wave disturbance in a medium is described by $y (x, t) = 0.02 \cos (50 π t + \frac{π}{2}) \cos (10 π x)$ , where $x$ and $y$ are in metre and $t$ is in second.