Embibe Experts Solutions for Exercise 3: EXERCISE 14.3

A uniform string fixed at both ends is vibrating in $3^{\mathrm{rd} }$ harmonic and equation of vibration is $y=4( \mathrm{cm})\sin \left[\left(0.8{ \mathrm{cm}}^{-1}\right)x\right]\cos \left[\left(400\pi {\mathrm{s}}^{-1}\right)t\right]$
The length of the vibrating string is

If the speed of sound in air is $v$, then the minimum possible length of the closed end organ pipe which resonates to frequency $f$ will be

A pipe closed at one end produces a fundamental note of $412 \mathrm{Hz}$. It is cut into two pieces of equal length, then the fundamental notes produced by the two pieces are,

A cylindrical tube, open at both the ends, has a fundamental frequency $f$. The tube is dipped vertically in water so that half of its length is inside the water. The new fundamental frequency is

A tuning fork of frequency $500 \mathrm{Hz}$ is sounded on a resonance tube. The first and second resonances are obtained at $17 \mathrm{cm}$ and $52 \mathrm{cm}$. The velocity of sound is,

A longitudinal sound wave given by, $p=2.5\sin \frac{\mathrm{\pi }}{2}(x-600t)$, where $t$ is in second, is sent down a closed organ pipe. If the pipe vibrates in its second overtone, the length of the pipe is,