A standing wave $y=A \sin \left(\frac{20}{3} \pi x\right) \cos (1000 \pi t)$ is maintained in a taught string, where $y$ and $x$ are in metres. The distance between two successive points oscillating with the amplitude $\frac{A}{2}$ across a node is

The fundamental frequency of an open organ pipe is $600 \mathrm{~Hz}$. The first overtone of this pipe has same frequency as first overtone of a closed organ pipe. If speed of sound is $330 \mathrm{~m} / \mathrm{s}$, then the length of a closed organ pipe is

The wavelength of two waves are 40 and $42 \mathrm{~cm}$ respectively. If the temperature of the room is $20^{\circ} \mathrm{C}$ then what will be the number of beats produced per second by these waves. When the speed of sound at $0^{\circ} \mathrm{C}$ is $332 \mathrm{~m} / \mathrm{s}$ ?

When a string is divided into four segments of $l_1, l_2, l_3$ and $l_4$. The fundamental frequencies of these three segments are $v_1, v_2, v_3$ and $v_4$, respectively. The original fundamental frequency $(v)$ of the string is

In a resonance coloum first and second resonance are obtained at depths 24 cm and 78 cm the third resonance will be obtained at depth.

A submarine A travelling at 17 m/s is being chased along the line of its velocity by another submarine B travelling at 34 m/s. B sends a sonar signal of 600 Hz to detect A and receives a reflected sound of frequency $\nu$. The of $\nu$ is

[Speed of sound in water = 1500 ms^$-$1]

Transverse waves of the same frequency are generated in two steel wires A and B. The diameter of A is twice that of B and the tension in A is half that in B. The ratio of the velocities of the waves in A and B is

In the diagram shown below, both the strings AB and CD are made of same material and have same cross-section. The pulleys are light and fictionless. If the speed of wave in string AB is v₁ and in CD is v₂, then ${{{v_1}} \over {{v_2}}}$ is

The equation of progressive wave is given by $Y = \sin \left[ {x\left( {{t \over 5} - {x \over 9}} \right) + {\pi \over 6}} \right]$ cm. Which one of the following is correct?

Two cars approach a stationary observer from opposite sides as shown in the figure.

The observer hears no beats. If the frequency of the horn of the car B is 504 Hz, then the frequency of the horn of the car A will be

The vibrations of a string of length 60 cm fixed at both ends are represented by the equation

$y = 4\sin \left( {{{\pi x} \over {15}}} \right)\cos (96\pi t)$

where x and y are in cm and t is in second. Calculate the velocity of the particle at x = 7.5 cm at t = 0.25 s.