NUMERICALS

A tuning fork of frequency $660 \mathrm{Hz}$ is vibrated just above a pipe of length $75 \mathrm{cm}$ filled with water. Water is gradually taken out of the tube. Find two positions of resonance from the upper end of the tube. Speed of sound in air is $330 \mathrm{m}/\sec$.

When a sound source of frequency $300 \mathrm{Hz}$ is held near the open end of a closed pipe, a loud sound is emitted from die pipe. Calculate the minimum length of the pipe and two other frequencies which may sound the pipe. Speed of sound$=330 {\mathrm{ms}}^{-1}$.

A pipe closed at one end is in resonance of a vibrating tuning fork when the length of the air column is $25 \mathrm{cm}$. The next resonance occurs when the length of the air column is $77 \mathrm{cm}$. If the speed of sound in air be $338 {\mathrm{ms}}^{-1}$, then calculate the wavelength of the emitted note and the frequency of the fork.

In a resonance tube, the first and the second resonances are obtained at $22.5$ $\mathrm{cm}$ and $70.0 \mathrm{cm}$ respectively. Find out the end-correction and the length of the air column for the third resonance.

 A $25 \mathrm{cm}$ long-closed organ pipe resonates with a tuning fork at $40°\mathrm{C}$. Determine the frequency of the fork. The speed of sound in air at $0°\mathrm{C}$ is $330 {\mathrm{ms}}^{-1}$.

The length of a pipe open at both ends is $48.8 \mathrm{cm}$ and its fundamental frequency is $320 \mathrm{Hz}$. Find the radius of the pipe.
If one end of the pipe be closed, what will be the fundamental frequency? (Speed of sound$=320 {\mathrm{ms}}^{-1}$.)

The smallest length of a resonance tube closed at one end is $32.0 \mathrm{cm}$ when it is sounded with a tuning fork of frequency $256 \mathrm{Hz}$ and $20.8 \mathrm{cm}$ when sounded with a fork of frequency $384$. Calculate the speed of sound and the end-correction.

A $0.75 \mathrm{cm}$ long closed organ pipe is vibrating in its fundamental mode. If the temperature of the room be $15°\mathrm{C}$ and the speed of sound in air at this temperature be $340 {\mathrm{ms}}^{-1}$, then determine the frequency of the note of the pipe. If the temperature rises to $25°\mathrm{C}$, then what will be the frequency? Consider the effect of temperature on the length of the pipe negligible.