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 :

(1) Zero

(2) π/2

(3) π

(4) 3π/2

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 :

(1) 10⁴ m/s

(2) 1 m/s

(3) 10^–4 m/s

(4) Not derivable from the above data

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

(1) $\frac{20}{n}$

(2) $\frac{10}{n}$

(3) $\frac{5}{n}$

(4) $\frac{n}{10}$

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 :

(1) Z₁ and Z₂

(2) Z₁ and Z₄

(3) Z₂ and Z₃

(4) Z₃ and Z₄

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 :

(1) ct / π

(2) ct / 2π

(3) π / 2k

(4) π / k

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

(1) $\frac{l}{4}$

(2) $\frac{l}{2}$

(3) l

(4) 2l

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 :

(1) 64

(2) 256

(3) 512

(4) 1024

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 :

(1) 2 Hz

(2) 4 Hz

(3) 5 Hz

(4) 10 Hz

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 :

(1) 10

(2) 0.5

(3) 1

(4) 0.117

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

(1) $\lambda =\frac{n^2}{2l}$

(2) $\lambda =\frac{l^2}{2n}$

(3) $\lambda =\frac{2l}{n}$

(4) $\lambda =2ln$