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 ..... $\%$
$30$
$20$
$69$
$\sqrt {69 } $
A wave on a string is travelling and the displacement of particles on it is given by $x = A\, sin\, (2t -0.1\, x)$. Then the wavelength of the wave is
Vibrating tuning fork of frequency $n$ is placed near the open end of a long cylindrical tube. The tube has a side opening and is fitted with a movable reflecting piston. As the piston is moved through $8.75 cm$, the intensity of sound changes from a maximum to minimum. If the speed of sound is $350 \,m/s. $ Then $n$ is .... $Hz$
The pattern of standing waves formed on a stretched string at two instants of time are shown in figure. The velocity of two waves superimposing to form stationary waves is $360$ $\mathrm{ms}^{-1}$ and their frequencies are $256$ $\mathrm{Hz}$.
$(a)$ Calculate the time at which the second curve is plotted.
$(b)$ Mark nodes and antinodes on the curve.
$(c)$ Calculate the distance between $\mathrm{A}^{\prime}$ and $\mathrm{C}^{\prime}$.
A sonometer wire oflength $1.5\ m$ is made of steel. The tension in it produces an elastic strain of $1 \%$. What is the fundamental frequency of steel if density and elasticity of steel are $7.7 \times 10^3 $ $kg/m^3$ and $2.2 \times 10^{11}$ $N/m^2$ respectively?
In order to double the frequency of the fundamental note emitted by a stretched string, the length is reduced to $\frac{3}{4}$$^{th}$ of the original length and the tension is changed. The factor by which the tension is to be changed, is