A perfectly elastic uniform string is suspended vertically with its upper end fixed to the ceiling and the lower end loaded with the weight. If a transverse wave is imparted to the lower end of the string, the pulse will
not travel along the length of the string
travel upwards with increasing speed
travelled upwards with constant acceleration
both $(B)$ and $(C)$
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 $20 \mathrm{~cm}$ 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.
Mechanical wave (sound wave) in a gas is
The speed of a transverse wave passing through a string of length $50 \;cm$ and mass $10\,g$ is $60\,ms ^{-1}$. The area of cross-section of the wire is $2.0\,mm ^{2}$ and its Young's modulus is $1.2 \times 10^{11}\,Nm ^{-2}$. The extension of the wire over its natural length due to its tension will be $x \times 10^{-5}\; m$. The value of $x$ is $...$
A uniform string oflength $20\ m$ is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the supports is (take $g= 10 $ $ms^{-2}$ )