Mechanical waves on the surface of a liquid are

If the initial tension on a stretched string is doubled, then the ratio of the initial and final speeds of a transverse wave along the string is :

One insulated conductor from a household extension cord has a mass per unit length of $μ.$ A section of this conductor is held under tension between two clamps. A subsection is located in a magnetic field of magnitude $B$ directed perpendicular to the  length of the cord. When the cord carries an $AC$ current of $"i"$ at a frequency of $f,$ it  vibrates in resonance in its simplest standing-wave vibration state. Determine the  relationship that must be satisfied between the separation $d$ of the clamps and the tension $T$ in the cord.

Equation of travelling wave on a stretched string of linear density $5\,g/m$ is $y = 0.03\,sin\,(450\,t -9x)$ where distance and time are measured in $SI$ united. The tension in the string is ... $N$

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.

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