SATHEE: Wave Motion 2 Question 3

Wave Motion 2 Question 3

3. A string is clamped at both the ends and it is vibrating in its 4 th harmonic. The equation of the stationary wave is $Y = 0.3 \sin (0.157 x) \cos (200 π t)$ . The length of the string is (All quantities are in SI units)

(Main 2019, 9 April I)

(a) $60 m$

(b) $40 m$

(d) $20 m$

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Answer:

Correct Answer: 3. (c)

Solution:

Given equation of stationary wave is

$Y = 0.3 \sin (0.157 x) \cos (200 π t)$

Comparing it with general equation of stationary wave, i.e. $Y = a \sin k x \cos ω t$ , we get

$\begin{aligned} k & = (\frac{2 π}{λ}) = 0.157 \\ \Rightarrow & λ & = \frac{2 π}{0.157} = 4 π^{2} (∵ \frac{1}{2 π} \approx 0.157) . \\ and & ω & = 200 π = \frac{2 π}{T} \Rightarrow T = \frac{1}{20} s \end{aligned}$

As the possible wavelength associated with $n$ th harmonic of a vibrating string, i.e. fixed at both ends is given as

$λ = \frac{2 l}{n} or l = n (\frac{λ}{2})$

Now, according to question, string is fixed from both ends and oscillates in 4th harmonic, so

$4 (\frac{λ}{2}) = l \Rightarrow 2 λ = l$

or $l = 2 \times 4 π^{2} = 8 π^{2}$ [using Eq. (i)]

Now, $π^{2} \approx 10 \Rightarrow l \approx 80 m$

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Wave Motion 2 Question 3

3. A string is clamped at both the ends and it is vibrating in its 4 th harmonic. The equation of the stationary wave is $Y = 0.3 \sin (0.157 x) \cos (200 π t)$ . The length of the string is (All quantities are in SI units)

Answer:

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Wave Motion 2 Question 3

3. A string is clamped at both the ends and it is vibrating in its 4 th harmonic. The equation of the stationary wave is Y=0.3sin⁡(0.157x)cos⁡(200πt). The length of the string is (All quantities are in SI units)

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

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3. A string is clamped at both the ends and it is vibrating in its 4 th harmonic. The equation of the stationary wave is $Y = 0.3 \sin (0.157 x) \cos (200 π t)$ . The length of the string is (All quantities are in SI units)