# The equation of a stationary wave is given as $\mathrm{y}=\mathrm{A}$ $\mathrm{sin}$ $0.5\mathrm{\pi t}$ $\mathrm{cos}\left(0.2\mathrm{\pi x}\right),$  where t is in seconds and x in centimetres. Which of the following is correct? 1. Wavelength of the component waves is 10 cm. 2. The separation between a node and the nearest antinode is 2.5 cm. 3. Frequency of the component wave is 0.25 Hz. 4. All of these

Subtopic:  Standing Waves |
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The equation of a travelling wave is given as $$y = A\sin(40\pi t-0.2\pi x),$$ where $$t$$ is in seconds and $$x$$ in metres. The minimum distance between two particles oscillating in the same phase is:
1. $$10~\text{m}$$
2. $$5~\text{m}$$
3. $$2~\text{m}$$
4. $$1.5~\text{m}$$
Subtopic:  Wave Motion |
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Two sound waves given by the equations $$y=A\sin 122 \pi t$$ and $$y=A\sin 128 \pi t$$ pass through a point simultaneously. The number of beats per second is:

 1 $$6$$ 2 $$5$$ 3 $$4$$ 4 $$3$$
Subtopic:  Beats |
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The graph between fundamental frequency ($$f$$) and corresponding tension ($$T$$) in a sonometer wire is best-represented by:

 1 2 3 4
Subtopic:  Travelling Wave on String |
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Stationary waves are formed on a stretched string. If the wavelength is $\mathrm{\lambda }$, then the distance between two points having the maximum displacement can be:

 1 3λ/2 2 4λ 3 5λ/2 4 All of these
Subtopic:  Standing Waves |
66%
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Given the equation for a wave on the string, $$y = 0.5\sin(5x-3t)$$ where $$y$$ and $$x$$ are in metres and $$t$$ in seconds, the ratio of the maximum speed of particle to the speed of wave is:
 1 $$1:1$$ 2 $$5:2$$ 3 $$3:2$$ 4 $$4:5$$
Subtopic:  Wave Motion |
83%
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If the transverse displacement of a string clamped at both ends is given by y(x,t)=12(cm) sin(6.28x)cos(3.14 t), where x is in cm and t is in seconds, then which of the following is not true?

 1 The velocity of the component wave is 0.5 cm/s. 2 The amplitude of one of the component waves is 6 cm. 3 The distance between two consecutive nodes is 0.5 cm. 4 x= 0.25 cm is the first node except the nodes at the ends.

Subtopic:  Standing Waves |
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Given below are two statements:

 Statement I: With the displacement wave we can produce a pressure wave. Statement II: Displacement and pressure waves both are having a phase difference of $$\frac{\pi }{2}$$.

 1 Statement I is incorrect and Statement II is correct. 2 Both Statement I and Statement II are correct. 3 Both Statement I and Statement II are incorrect. 4 Statement I is correct and Statement II is incorrect.
Subtopic:  Pressure Wave in Sound |
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A string of length l is fixed at one end and free at the other. If it resonates in different modes, then the ratio of frequencies is:

1. 1:2:3: ......

2. 1:3:5:7: ......

3. 1:2:4:8: ..........

4. 1:3:9: ........

Subtopic:  Standing Waves |
82%
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A sound wave is passed through a chamber. If the r.m.s. speed of molecules in a gas is v1 and the speed of sound is v2 in the gas, then:

 1 v1 = v2 2 v1 > v2 3 v1 < v2 4 v1 ≤ v2
Subtopic:  Speed of Sound |
64%
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