The distance between the nearest node and antinode in a stationary wave is :

For the stationary wave $y=4\sin \left(\frac{{\displaystyle \pi x}}{{\displaystyle 15}}\right)\cos \left(96\pi t\right)$, the distance between a node and the next antinode is :

The equation of a stationary wave is $y=0.8\cos \left(\frac{{\displaystyle \pi x}}{{\displaystyle 20}}\right)\sin 200\pi t$, where x is in cm and t is in sec. The separation between consecutive nodes will be :

A wave represented by the given equation $y=a\cos (kx-\omega t)$ is superposed with another wave to form a stationary wave such that the point x = 0 is a node. The equation for the other wave is :

A standing wave having 3 nodes and 2 antinodes is formed between two atoms having a distance 1.21 Å between them. The wavelength of the standing wave is :

In stationary waves, the distance between a node and its nearest antinode is 20 cm. The phase difference between two particles having a separation of 60 cm will be :

A standing wave is represented by

$Y=A\sin \left(100t\right)\cos (0.01x)$

where Y and A are in millimetre, t is in seconds and x is in metre. The velocity of the wave is :

Two waves are approaching each other with a velocity of 20 m/s and frequency n. The distance between two consecutive nodes is :

The following equations represent progressive transverse waves $Z_1=A\cos (\omega t-kx)$, $Z_2=A\cos (\omega t+kx)$, $Z_3=A\cos (\omega t+ky)$ and $Z_4=A\cos (2\omega t-2ky)$. A stationary wave will be formed by superposing :

Two traveling waves $y_1=A\sin \left[k\right(x-ct\left)\right]$ and $y_2=A\sin \left[k\right(x+ct\left)\right]$ are superimposed on the string. The distance between adjacent nodes is :

A string fixed at both ends is vibrating in two segments. The wavelength of the corresponding wave is :

A 1 cm long string vibrates with the fundamental frequency of 256 Hz. If the length is reduced to $\frac{1}{4}cm$  keeping the tension unaltered, the new fundamental frequency will be :

Standing waves are produced in a 10 m long stretched string. If the string vibrates in 5 segments and the wave velocity is 20 m/s, the frequency is :

A string is producing transverse vibration whose equation is $y=0.021\sin (x+30t)$, Where x and y are in meters and t is in seconds. If the linear density of the string is 1.3×10^–4 kg/m, then the tension in the string in N will be :

A stretched string of length l, fixed at both ends can sustain stationary waves of wavelength λ, given by 

A string on a musical instrument is 50 cm long and its fundamental frequency is 270 Hz. If the desired frequency of 1000 Hz is to be produced, the required length of the string is :

The tension in a piano wire is 10N. What should be the tension in the wire to produce a note of double the frequency :

A string of 7 m length has a mass of 0.035 kg. If the tension in the string is 60.5 N, then the speed of a wave on the string is :

A second harmonic has to be generated in a string of length l stretched between two rigid supports. Distances from one end where the string has to be plucked and touched are :

The tension of a stretched string is increased by 69%. In order to keep its frequency of vibration constant, its length must be increased by :

The length of a sonometer wire tuned to a frequency of 250 Hz is 0.60 metre. The frequency of tuning fork with which the vibrating wire will be in tune when the length is made 0.40 metre is :

Two uniform strings A and B made of steel are made to vibrate under the same tension. If the first overtone of A is equal to the second overtone of B and if the radius of A is twice that of B, the ratio of the lengths of the strings is -

Two wires are fixed in a sonometer. Their tensions are in the ratio 8 : 1. The lengths are in the ratio 36 : 35. The diameters are in the ratio 4 : 1. Densities of the materials are in the ratio 1 : 2. If the lower frequency in the setting is 360 Hz. the beat frequency when the two wires are sounded together is :

The first overtone of a stretched wire of given length is 320 Hz. The first harmonic is : 

The sound carried by the air from a sitar to a listener is a wave of the following type :

Three similar wires of frequency n₁, n₂ and n₃ are joined to make one wire. Its frequency will be :

Two vibrating strings of the same material but lengths L and 2L have radii 2r and r respectively. They are stretched under the same tension. Both the strings vibrate in their fundamental modes, the one of length L with frequency n₁ and the other with frequency n₂. The ratio n₁/n₂ is given by :

A string of length 2 m is fixed at both ends. If this string vibrates in its fourth normal mode with a frequency of 500 Hz then the waves would travel on its with a velocity of :

The fundamental frequency of a sonometre wire is n. If its radius is doubled and its tension becomes half, the material of the wire remains same, the new fundamental frequency will be :

In an experiment with a sonometer, a tuning fork of frequency 256 Hz resonates with a length of 25 cm and another tuning fork resonates with a length of 16 cm. The tension of the string remaining constant the frequency of the second tuning fork is :