B M Sharma Solutions for Chapter: Superposition and Standing Waves, Exercise 2: CONCEPT APPLICATION EXERCISE

A tube closed at one end has a vibrating diaphragm at the other end, which may be assumed to be a displacement node. It is found that when the frequency of the diaphragm is $2000 \mathrm{Hz},$ a stationary wave pattern is set up in which the distance between adjacent nodes is $8 \mathrm{cm}.$ When the frequency is gradually reduced, the stationary wave pattern disappears but another stationary wave pattern reappears at a frequency of $1600 \mathrm{Hz}.$ Calculate the distance between the diaphragm and the closed-end, 

A tube closed at one end has a vibrating diaphragm at the other end, which may be assumed to be a displacement node. It is found that when the frequency of the diaphragm is $2000 \mathrm{Hz},$ a stationary wave pattern is set up in which the distance between adjacent nodes is $8 \mathrm{cm}.$ When the frequency is gradually reduced, the stationary wave pattern disappears but another stationary wave pattern reappears at a frequency of $1600 \mathrm{Hz}.$ Calculate the next lower frequencies at which stationary wave patterns will be obtained.

The first overtone of a pipe closed at one of its end is $900 \mathrm{Hz}.$ Find the fundamental frequency of this pipe open at both ends.

An organ pipe has two successive harmonics with frequencies $1372$ and $1764 \mathrm{Hz}.$ Find these harmonics and the length of the rube. Assume the sound speed $v=330 \mathrm{m} {\mathrm{s}}^{-1}$

A tuning fork with a frequency of $f=500 \mathrm{Hz}$ is placed near the top of the tube shown in figure. The water level is lowered so that the length $L$ slowly increases from an initial value of $20.0 \mathrm{cm}.$ Determine the next two values of $L$ that correspond to resonant modes. Assume the sound speed $v=320 \mathrm{m} {\mathrm{s}}^{-1}$

In the given figure, water is being pumped into a tall, vertical cylinder at a volume flow rate $R.$ The radius of the cylinder is $r,$ and at the open top of the cylinder a tuning fork is vibrating with a frequency $f.$  As the water rises, what time interval elapses between successive resonances?

A student is listening to the sounds from an air column that is $0.70 \mathrm{m}$ long. He doesn't know if the column is open at both ends or open at only one end. He hears resonance from the air column at frequencies $250 \mathrm{Hz}$ and $600 \mathrm{Hz}.$ Justify, why the above given situation is impossible.

A hard metallic rod fixed at one of its ends is fitted with a vibrator at the other end. The vibrator is electrically driven and sets up a longitudinal wave that moves along the rod. The waves get reflected at the fixed end $P.$ The reflected waves superimpose with the waves sent by the vibrator. For the resonance to occur, a strong longitudinal standing wave is generated in the rod. Find the frequency of the vibrator if the rod resonates with its $3^{\mathrm{rd}}$ overtone. [Put $\left.Y=6\times {10}^8 \mathrm{N} {\mathrm{m}}^{-2}, \rho =24 \mathrm{gm} {\mathrm{cc}}^{-1}, l=20 \mathrm{cm}\right]$