Revisiting Standing Waves

Q. An aluminium rod having length $100\text{cm}$ is clamped at its middle point and set into longitudinal vibrations. Let the rod vibrate in its fundamental mode. The density of aluminium is $2600{\text{kg/m}}^3$ and its Young's modulus is $7.8\times {10}^{10}{\text{N/m}}^2.$ The frequency of the sound produced is

1. $1250\text{Hz}$
2. $2738\text{Hz}$
3. $2350\text{Hz}$
4. $1685\text{Hz}$

Q.

A copper rod of length 1.0 m is clamped at its middle point. Find the frequencies between 20 Hz and 20, 000 Hz at which standing longitudinal waves can be set up in the rod. The speed of sound in copper is $3.8km{s}^{-1}$

1. $n\times 1.9kHz$

   $n=1,2,\mathrm{3.....}10$

2. $n\times 3.1kHz$

   $n=1,2,3,4,5,6$

3. $n\times 5kHz$

   $n=1,2,3,4$

4. None of these

Q.

The separation between a node and the next antinode in a vibrating air column is 25 cm. If the speed of sound in air is 340 $m{s}^{-1}$, find the frequency of vibration of the air column

1. 340 Hz

2. 240 Hz

3. 575 Hz

4. 670 Hz

Q.

Consider the following statements about sound passing through a gas.

(A) The pressure of the gas at a point oscillates over time.

(B) The position of a small layer of the gas oscillates over time.

1. Both A and B are correct.

2. A is correct but B is wrong

3. B is correct but A is wrong.

4. Both A and B are wrong.