A $20 \mathrm{~cm}$ long string, having a mass of $1.0 \mathrm{~g}$, is fixed at both the ends. The tension in the string is $0.5 \mathrm{~N}$. The string is set into vibrations using an external vibrator of frequency $100 \mathrm{~Hz}$. Find the separation (in $cm$) between the successive nodes on the string.

A heavy ball of mass $M$ is suspended from the ceiling of car by a light string of mass $m (m << M)$. When the car is at rest, the speed of transverse waves in the string is $60\, ms^{-1}$. When the car has acceleration $a$ , the wave-speed increases to $60.5\, ms^{-1}$. The value of $a$ , in terms of gravitational acceleration $g$ is closest to

A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of $45 \;Hz$. The mass of the wire is $3.5 \times 10^{-2} \;kg$ and its linear mass density is $4.0 \times 10^{-2} \;kg m ^{-1} .$ What is

$(a) $ the speed of a transverse wave on the string, and

$(b)$ the tension in the string?

The linear density of a vibrating string is $1.3 \times 10^{-4}\, kg/m.$ A transverse wave is  propagating on the string and is described by the equation $Y = 0.021\, \sin (x + 30t)$ where $x$ and $y$ are measured in meter and $t$ in second the tension in the  string is ..... $N$

A uniform rope having some mass hanges vertically from a rigid support. A transverse wave pulse is produced at the lower end. The speed $(v)$ of the wave pulse varies with height $(h)$ from the lower end as:

The transverse displacement of a string (clamped at its both ends) is given by

$y(x, t)=0.06 \sin \left(\frac{2 \pi}{3} x\right) \cos (120 \pi t)$

where $x$ and $y$ are in $m$ and $t$ in $s$. The length of the string is $1.5\; m$ and its mass is $3.0 \times 10^{-2}\; kg$

Answer the following:

$(a)$ Does the function represent a travelling wave or a stationary wave?

$(b)$ Interpret the wave as a superposition of two waves travelling in opposite directions. What is the wavelength, frequency, and speed of each wave?

$(c)$ Determine the tension in the string.