Progressive waves and the principle of superposition — practice questions

Question 1 · difficulty L2 · understanding

A transverse wave on a string is described by $y=3 \sin (36 t+0.018 x+\pi / 4)$. where $x, y$ are in cm and $t$ in seconds. The least distance between the two successive crests in the wave is $\_\_\_\_$ cm . (Nearest integer) $$(\pi=3.14)$$

Question 2 · difficulty L2 · understanding

Two open organ pipes of lengths $$60 \mathrm{~cm}$$ and $$90 \mathrm{~cm}$$ resonate at $$6^{\text {th }}$$ and $$5^{\text {th }}$$ harmonics respectively. The difference of frequencies for the given modes is _________ $$\mathrm{Hz}$$. (Velocity of sound in air $$=333 \mathrm{~m} / \mathrm{s}$$)

Question 3 · difficulty L2 · understanding

A sonometer wire of resonating length $$90 \mathrm{~cm}$$ has a fundamental frequency of $$400 \mathrm{~Hz}$$ when kept under some tension. The resonating length of the wire with fundamental frequency of $$600 \mathrm{~Hz}$$ under same tension _______ $$\mathrm{cm}$$.

Question 4 · difficulty L2 · understanding

A point source is emitting sound waves of intensity $$16 \times 10^{-8} \mathrm{~Wm}^{-2}$$ at the origin. The difference in intensity (magnitude only) at two points located at a distances of $$2 m$$ and $$4 m$$ from the origin respectively will be _________ $$\times 10^{-8} \mathrm{~Wm}^{-2}$$.

Question 5 · difficulty L2 · understanding

The fundamental frequency of vibration of a string stretched between two rigid support is $50 \mathrm{~Hz}$. The mass of the string is $18 \mathrm{~g}$ and its linear mass density is $20 \mathrm{~g} / \mathrm{m}$. The speed of the transverse waves so produced in the string is ___________ $\mathrm{ms}^{-1}$

Question 6 · difficulty L2 · understanding

In an experiment with sonometer when a mass of $$180 \mathrm{~g}$$ is attached to the string, it vibrates with fundamental frequency of $$30 \mathrm{~Hz}$$. When a mass $$\mathrm{m}$$ is attached, the string vibrates with fundamental frequency of $$50 \mathrm{~Hz}$$. The value of $$\mathrm{m}$$ is ___________ g.

Question 7 · difficulty L2 · understanding

The equation of wave is given by $$\mathrm{Y}=10^{-2} \sin 2 \pi(160 t-0.5 x+\pi / 4)$$ where $$x$$ and $$Y$$ are in $$\mathrm{m}$$ and $$\mathrm{t}$$ in $$s$$. The speed of the wave is ________ $$\mathrm{km} ~\mathrm{h}^{-1}$$.

Question 8 · difficulty L2 · understanding

A transverse harmonic wave on a string is given by $$y(x,t) = 5\sin (6t + 0.003x)$$ where x and y are in cm and t in sec. The wave velocity is _______________ ms$$^{-1}$$.

Question 9 · difficulty L2 · understanding

The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pipe is 20 cm. The length of the open organ pipe is _____________ cm.

Question 10 · difficulty L2 · understanding

The amplitude of wave disturbance propagating in the positive x-direction is given by $$y = {1 \over {{{(1 + x)}^2}}}$$ at time t = 0 and $$y = {1 \over {1 + {{(x - 2)}^2}}}$$ at t = 1 s, where x and y are in metres. The shape of wave does not change during the propagation. The velocity of the wave will be ___________ m/s.